How dense are the roots in the soil? Are you saying "rootbound" because the roots line the pot, reflecting its shape? If the roots are very dense in the soil, I'd repot it. Don't put it in a drastically larger pot, but loosen some of the roots as you would for any other plant.

Happy growing!

Here is a link that might be useful: Fred's Begonias

OMG...I'm a plant addict!...2 yrs ago..orchids..and last fall, my adopted plumeria (about to bloom), so had to adopt another! Picked up a Rex begonia last week...I'm in love...so hit a local garden center yesterday in search of!! Found 2 beauties... Fred..your picture "book"...so incredible...if I may say, your Unk4885 looks exactly like one I purchased yesterday called "Shirley". Another I brought home yesterday is called "Snow White"... the orig one I purchased last week had no name, but looks so much like one you call "Shirtsleeves"... I will have to buy another house to make room for my "addiction." That of course, doesn't even speak to the many other assorted beauties I have! So glad to see everyone else's gorgeous specimens! Now I have 3 forums to check in on! Fred, thanks, for sharing your pics! Is there a general word or 2 of advice that would help in keeping my babies happy and healthy? I could not, as I read somewhere (?), snip off the few lovely flowers from my Shirley!...she's just as beautiful with them! Thanks for any and all advice, Eileen

PS...Had an "Angel Wing" years and years ago!...Will have to bring another into my life!