Answer
126
Work Step by Step
There are $2^n$ bit strings of length n [n choices each with two options]
Thus the number of bit strings of length six or less, not counting the empty string = $2^1+2^2+2^3+2^4+2^5+2^6$
=$2+4+8+16+32+64$
=126
[The sum could also have been calculated by using Geometric Progression]