I've been messing about with my CNC machine and got decent results in the practice runs but I've got a question concerning swapping bits for multiple toolpaths in one job.

Once I zero the z-axis for one bit and run that toolpath, when I switch the bit I have to zero for that bit and it's always off by a smidgen.

I'd like to collar the bits so I don't have to re-zero for each bit. Should I get "bearing lock collars" for the bits? Is that the correct solution?

Yes.

Big autochange CNC's have various bits already measured and entered into the controller. Each has it's own toolholder. You need to do something similar. Measuring a bit length, either by caliper or touchoff, is not foolproof. You might test each bit after they are measured to be sure. Take it out and back in to see if it duplicates. I worked in wood, so we did not have to be too accurate.