Service bulletin compliance constitutes maintenance, hence must be logged. If it is, for example, a Rotax service bulletin, it goes in the engine logbook. A Skycatcher SB, OTOH, goes into the airframe logbook, a Sensenich SB goes into the prop logbook, and a Dynon SB gets entered into the Avionics logbook. If you don't have separate prop and avionics logbooks (which is a good idea, but not required), those would go in the airframe logbook.
Logbook entries have to be made at the time the work is performed. They must include the aircraft make, model, serial number and registration, the date, total hours in service, name of the person complying, and his or her certificate type, number, and (if applicable) expiration date. Here's an example of the kind of form (sticker or stamp) as shop might use for such an entry:
Similarly, a Condition Inspection logbook entry should look like this:
