If bachelor were a noun functioning as a modifier, it would not need the possessive ' 's ' (i.e. a bachelor degree ) (another example: a flower shop; flower modifying shope)
However, if it needs a possessive 's' to carry out its modifying function, I am curious why it shouldn't be s'?
E.g. The three sisters' bags is right
The three sister's bags is wrong
?
In your last example, "three" refers to "sisters", so the bags belong to those three sisters. In the original example the noun is a "bachelor's degree". If you have three of them, you don't have three batchelors, you have three degrees.