"There didn't use to be." This is the proper answer. You need an auxiliary verb which takes both the negative and the tense.

A is technically correct. You can also try: -> There never used to be -> There used not to be

Negation of something that happens usually is quite tricky, as the negation could mean different things; Logically I would say: -- it isn't that there used to be ... Although it might be quite pedantic. Or , changing the verb: -- it didn't usually happen that ... I will not pick any of (a), (b), (c).

Neither of the above. The negation of "There used to be" can be done by adding "never" in front of "used to": - It never used to be like this. - He never used to play this song before. - We never used to go out when we were together. But if you want to say that you are not used to something else, then just negate the verb "to be": - I am not used to hearing you yell. - He isn't used to speaking in front of a group. - We aren't used to singing this song together. I hope this helps :)