You are quite correct in saying that budgies can be little bullies! My cockatiel Fang is more the shy, retiring type, whereas Valentino the budgie is somewhat more the "in your face" type, although it must be said that now he is a little older he has mellowed quite a bit. Your prospective budgie being a bit older may be a little calmer too, although as my vet is fond of saying "budgies can be like that pesky little brother who gets in your face and doesn't know when to quit!" You also need to think about how the introduction of another bird may impact on the dynamic that you currently have between you and your cockatiel. Individual results always vary on that front! Personally I would try to have the budgie health checked as soon as practicable to ensure he is not bringing any health nasties with him too.
Having said all that, I think as you are not planning on caging them together and they are given adequate supervision particular in the initial stages they will very likely be fine together. Budgies and cockatiels are a pairing that often works out very well indeed. Not
every time necessarily of course, so you do need to be prepared for that, but in my personal experience having had that combination for many years, most of the time they are pretty good together.