Is it common to have your baby tooth removed and adult tooth bridged?

Yes. But nowadays it is also common to place a dental implant. It depends on the amount of space available and the condition of the adjacent teeth. Ask your dentist what is best for you.
Nowadays. It was more common years ago before the reliability & long term success of dental implants. Nowadays, the standard of care, when possible is to remove the baby tooth & replace it with an implant retained crown (assuming there is sufficient room for the new crown & the roots of the adjacent teeth are far enough apart for the proper placement of a dental implant. Sometimes some orthodontics also.
Common. Dr davantzis is correct. But also understand that baby molars are wider that the permanent premolars that are supposed to replace them. So if you still have a baby tooth present, and no underlying permanent tooth, the adjacent teeth may be slightly out of position. It may be wise to have an orthodontist position the adjacent teeth properly before doing replacement. Get an evaluation before rx.