No, each hash function tells you a bit to set. Your hash functions each take an input object and return a location in the vector. That location is set to 1.

With regards how big to make things, you need to do the math. If you have a vector of 1000 bits in your vector and you have 10 hash functions then there are 1000^10 = 10^30 possible collections of ten bits that can be set. If your plausible collection is only of size a few billion then coincidences won't be common or frequent.

256 bytes is 2048 bits, 16 hash functions, suddenly there are 2048^16 possible combinations, or 2^176 which is about 10^50.