So... If I went to law school would I be able to get into this field with a B.S.?
It is possible . . . just more difficult. It will be particularly difficult for you since your degree is bio oriented, because most bio clients want PhD's working on their apps whenever possible.
Of course, these comments relate to patent proseuction and not patent litigation. There are many attorneys practicing patent litigation who have no science background whatsoever.
To add to the comments above, I have a BS in chemistry and broke into the field by working at the PTO. You could try the same, but I think even the PTO wants Bio examiners to have some form of an advanced degree.