Basically, the integer type determines the integer type of the underlying vector of numbers representing the bits. You can think that if you have a bitvec of u16, then it will have a "slice" of u16's, while if you have a u64, you'll have a slice of u64's.
There may be marginal differences in speed, for cumulative lookups, such as count or find first 0.
I tend to just stick a usize and be done with it. If you profile and discover that it really matters, then you can go ahead and benchmark. Otherwise, just use usize.