How does bed bath and beyond choose its merchandise and products? How can I get my product seen by them?

They have buyers located at their corporate office. These are the people you want to talk to. The thing to remember is they, like any other big box chain, are looking for established suppliers (not designers). If you already have your product made over seas (for dirt cheap) and a distribution center, then it is rather easy. If not, then you can ask to use one of theirs. The only problem with this, is they do not care if you turn a profit. As long as they get the product for cheap, on time, and without issues. You must make sure to cover all cost of yours to include the packaging and things before you settle on a price to them.