Paul Stoddart for FIA president; he knows how to get things done on a budget, Branson could run FOM via the Virgin group, it's not as if Bernie needs a direct successor, as long as the show goes on it does not need the single public figure to run it.
I imagine Beardy could appoint a team of people to oversee the running of the commercial aspects and ensure the best possible gains from tie in's with his T.V. channels, broadband provider, mobile phone network, book publishers etc. Also he has numerous possible tie ins with his other leisure products such as 'experience' days, travel and tourism, even health spa's and space flights (your co-pilot today is Rubens Barrichello!), he might even be able to do a deal on air freighting all their crap around, at the very least he could fly the team staff and drivers from race to race, probably with a heavy dose of publicity.
In reality though we are as likely to see Zippy, Bungle and George in charge.