Which one of these sentences is correct?
- I don't bother to study.
- I don't bother studying.
Antony Quinn is correct, but I think it could do with a little more explanation.
No. 1 is perfectly understandable, but would not be used by a native English speaker. However, compare the following:
3) I won't bother to look for it
4) I won't bother looking for it
In my view 3 is just as acceptable as 4.
I think the difference in the two cases is to do with whether it is a specific or a general statement: to my intuition the "-ing" form is strongly preferred for a general sense, but not when a specific occasion is being referred to.
Also note that the almost synonymous phrase "can't be bothered" prefers the "to" form, though the "-ing" form is also found.
From my (UK) perspective, "bother to study" sounds correct, and "bother studying" sounds colloquial. However, the implied casualness of "I don't bother" seems to establish a preference for the colloquial version.