I agree with Victoria. Both are grammatically correct, but the one that fits here is "try not to blush."
However, I can think of a scenario in which "try not blushing" would work. Let's say this is the sixth interview with the same person and the interviewee has felt that the interviewer was looking at her strangely the first five times. Every time she tried to change something about her presentation but the strange looks were still there. She has noticed that she has blushed every time, so this time her friend tells her "Try not blushing; maybe that'll do the trick."