I can't answer your question directly. I expect the span tables can tell you; just make sure that you allow enough clearance above the door so that when the lintel is deflected downward a bit by the roof load, it doesn't compress the door. If the tables show that you need a deeper beam than you would like then you could consider a flitch beam (i.e. two thin wooden beams bolted either side of a steel plate, typically 10 mm steel). They are stiffer but still allow timber to timber fastenings. You do have to consider thermal bridging to avoid cold spots.

Check your bi-fold door make-up - I've been looking at one company - their wood framed bi-folds are hung from the top (i.e. the lintel has to take the load of the glass etc) - their aluminium bi folds support the glass at the bottom. It makes a big difference to the loading on the lintel or floor.

Ours is a house, so carrying much more on top. Though it also carries our top hung bifolding doors that are triple glazed and incredibly heavy.