hey there i have done several re-staining on pipes i will only use fiebings stain. its a leather stain that you can get at some hobby stores or shoe repair stores. its a great high quality stain that is alcohol based. dependings on the condition of the pipe you could sand it down all the way, however i personally do not always recommend this unless you want to go lighter in color. also is you were to remember to use the highest grit you can get, i use 1000 grit or higher, and always go with the grain. you can also use a good de-glosser, or anything that will remove the poly,wax, or what ever it is finish with. once you re stain use a heat source (flame, lighter,heat gun) over the bowl (without stem in it) heating sets the stain better,wipe excess off. repeat if desired. let dry overnight, then start polishing the bowl with a good carnuba wax. the more coats the better the look.
if its a rustic bowl you can do the same thing....trick for getting the finishing shine on these bowls is wax and then lightly heat the wax which will melt into the little areas.
good luck