As Jstern mentions denatured alcohol is great for cleaning up any shellac that ended up where you don't want it. Just dab a bit onto a rag and then wipe the rag over your trouble area.
I don't cover the bike, sometimes I'll mask my bar end shifter pods with blue painter's tape but I usually don't bother.
I haven't had any trouble handling the shellac, no issues with runs or drips. I use a 1" wide chip brush and always lay off my brush on the inside edge of the can. I clean my brush with denatured alcohol and have used the same cheap brush for many shellac applications over the last several years.
Be warned! Shellac can and does go bad. I pulled an old can of amber shellac out of our warehouse for my handlebars once. It never dried and was still tacky and goopy days later. I removed it with denatured alcohol. Better your bars than a furniture project!
It depends on the project but I typically like three coats of shellac.