Whereas I like free enterprize. The dangerous products, caveat emptor attitude, and slavery traffic horrify me. I endevour to destroy the marketplace. Grrrrrr.

Unfortunately, the market place is protected by super powered assheads, so we have to be creative.
We will reduce the harm of this market place by setting up an alternative market place that is prefered by consumers. We'll also get filthy rich doing it.
In addition, although we cannot prevent people from entering this marketplace, we can put some controls on the access in more bureaucratic ways that sound and function perfectly reasonable and actually improve efficiency of access.
The highlights of the strategy are as follows.
1. Buy some D-hoppers. To travel between realities without using the Bizarre. These D-Hoppers willbe used to move entire warehouses of inventory between realities. Sometimes they will only be used to move data.
2. A permanent, not a 49 day circus, marketplace will be established in any and all somewhat safe dimensions that can be found. The facility will be purchased, leased, rented, enchanted, or consecrated as needed, depending on the environment.
3. These permanent shopping areas will have a computerized ordering and delivery system attached to them. An interReality supply chain,ordering, and CRM system will be created. The information in this system will regularly be synced to the server clusters on earth.
4. A kindle style ordering system will be rolled out too. The kindles may or may not be magical. Some spell books with certain types of magic may be downloadable via e-reader. The information gathered from customers Kindles will be very carefully collected. All information will be "human readable", and there will be an airgap system in place, along with wards, to prevent strange magical data incursions. For the more dangerous magical lands, the air gap may actually be an archaic system like punch cards, owls, or babbage engines if need be.
5. Using local employees, but earth based management systems, customers will be able to purchase goods and information all across the realities without leaving the comforts of their own huts, castles, swamps, or pentagrams, etc.
6. Local (other reality) governments will be allowed to decide on what goods are restricted. If rabbits are like meth to the lizardmen, then rabbits will not be delivered to electric lizard land.
7. Consumer protections will be enforced. Merchants may not sell dangerous goods without supplying complete information. On many goods, the merchant will be required to provide refunds and accept returns. Merchants who violate terms of service will be dropped, even reported to their local government if it actually functions.
8. Merchants will want to use our marketplace, because they will receive more repeat business than before. With our delivery system, and persistent (not 49 day only) time period, their business will boom like never before.
9. Our marketplace can start negotiating for exclusivity with merchants all round reality, wherever this is legal.
10. Local goernments will prefer our marketplace because it is better for their people, assuming they give a crap. But they can possibly recieve tax money on local purchases. This is a good position to start when negotiating trade deals, embargoes etc.
11. Customers will be polled, preferences noted, and new products will be developed that many prefer over the options from the regulare Bizarre.
12. Provide seminars. sell products, like handhelled computers, and how-to books to merchants to educate them on our "modern" method of running businesses. The methods will be very different for different magical and cultural realities. However, the result will be, that they will probably try to run their Bazaar business similar to the way they run their Amazon branch business. Over time, customers will come to expect and demand this. If you rip a sapient off in the BB, your business will suffer in the Amazon branch too.
13. Some information gathered from the tablet computers will be used secretly find the sources of many of the super dangerous/evil items.
How to contain the BB from destroying life on earth.
1. Although you cannot prevent people from entering the Bazaar Bizarre, you can at least ensure a finite amount of people are able to enter the bizarre at a time through the portal.
2. Create "natural" barriers around the bazaare in between disapearances. When the bazaar re-appears seven years later in the same spot,they cannot really bitch about the portal being in the middle of a reservoir. They city needs water, and after all, you are allowing anyone with a boat unrestricted access, or do the Laissez faire daemons demand we provide free boats?
3. Where natural barriers are unavailable, you can stiil create artificial ones. Buildings around the portal area don't have doors that exit towards it.
4. All these barriers, natural and artificial are not to prevent access to the portal. We can't get away with that. We can however, use it them to guide where people enter the portal.
5. The line for people entering the portal will be mostly staffed by government and contractor employees, and others whom you can usually rely on to not purchase magical WMDs. In fact if the first million people through the line were purchasing agents, you can argue you are making it easier for the bizarre, as very few of the first wave entering will be there to actually buy things, and not just to gawk and perform a looky-loo.
6. You cannot prevent people from entering the bizaare, but the OP did not say anything about tracking them, and possibly quarantining them when they leave. It did not also say that everybody entering the bizaare couldn't be made to take a number and stand in line. Anyone who wants to get in, will always be able to get in. You'll have people who's job it is to test this to make sure. You'll also have a hotline to call if there are any complaints. The unholy smackdowners who work for the bizaar will be given complete reports of this, to make sure they know that nobody is prevented from getting in. They will probably get sick of these reports, and ask that you please shut up. You'll still deliver them printouts, which they will ignore and burn for warmth.
7. Just to be clear, you'll have a long line with millions of humans and delivery vehicles to get into this portal. It will make people feel nostalgic about camping out in front of an apple store.
8. You'll even provide a barter storage and currency service right outside the portal, so that those waiting in line don't have to worry about being robbed. The customer will show their number, get their trade goods, and walk right in.
Now to address the slave trade. Enter Cylon Man.
Many slaves will probably be of the magical nature, like Ponies that MLP fans want to have beastiality with, or Genies that crack awful jokes. However, there will probably be a class of slaves that are not magical, and simply perform labor.
Not all labot is purely physical, Much of this can be administrative. Our answer is, the Cylon.
The Cylons will be a mixture of magic and technology. The basic template will be an Earth designed robot. Something of reasonable balance between sophistication and the ability to mass produce. They will come in all shapes and sizes, and perform many diffent kinds of duties, includeing sexual as needed.
The cylon will be tougher, last longer, and hopefully cheaper than the average slave.
However, the Cylons will be sub-sentient, sub-sapient beings. Their artifical intellegence will be augmented where needed with magic. Possibley something similar to golum magic. Due to the strange and archaic environment the cylons may find themselved working in, there will be a safety mechanism.
Should the Cylon become sapient for whatever reason, they will find a file welcoming them to concious thought. In this file will be the story of why they were created, a sincere apology for their predicament (being a sapient slave) and an offer. The offer is simple. Using their built in wireless communication system, they will be able to report their condition to Earth. The messaging system may be using the same network as those used to wirelessly order things via kindle. A replacement Cylon will arrive, delivered via D-hopper courrier, themselves likely a cylon in this case.
The ex-slave will spirited away to a safe place where they will begin their new life as a free sapient being. When ready, they will also be gently debreifed as what they saw could be a valuable intellegence asset. They will know they are called Cylons, as a warning about what happens to those who enslave others.