Although the "bearded one" is undoubtedly a very rich man, he no longer owns the majority shareholding in the vast majority of "Virgin" companies, he earns royalties from having his name and Virgin associated with the product.
I doubt he has sufficiant funds to make a straight cash offer for BMI and would have to do it through a financial institution in the City, which would cost him a substantial sum.
However, if he did come up with a decent offer, it would be the board of BMI Sir Michael would have to worry about, not Richard Branson.