First of all, you said already cut the ticket, then why you are asking a question? Second, your information is incorrect, if you have only a B1 visa definitely they wouldn't allow entering the USA.
Third one if your parents are in B1/B2 ( I am not sure because you said only B1) it's up to you but you never know, if the immigration officer asks them to guarantee to return what they will show?
Note: My suggestion: do the round ticket which is very cheap for an international flight compare to one way, later you can change the date to 80-150 dollars. This is only my suggestion decision up to you