Help with gene linkage and mapping!
I think your reasoning is sound and your ordering very likely, but I wouldn't feel comfortable with deciding the side B is on. Actually, it's more than that: I think that by using basically the same number (~40) for everything that includes B, they want you to come to another conclusion.

Unlike eukaryotic cells undergoing meiosis, there is no crossing over in bacteria taking up DNA from the surroundings. Therefore, it shouldn't be possible for the cell to inherit A, B and C but not D, which is in the middle. Simply, from my understanding of the "experimental" setup, they added antibiotics A, B and C, so they have to assume the bacteria are wild type for D. However, it's basically for sure that those ABC-resistant colonies are also D-resistant.

Still, your reasoning is correct: comparing BC and AB should give you the side B is on, since the break could have been inside of the 3-gene cluster. However, the numbers are very close, and the "AB" and "BC" phenotypes are probably ABCD anyway, making the small difference even less meaningful (the true AB and BC are lost because they are mixed with the many ABCD).