Here's a closeup of the B.

Hmmm...something fishy about someone named Miller looking for the Budweiser font...

Most likely it's custom, but the lower-case is not extremely distinctive -- many formal scripts have similar forms. Check out Mike Yanega's site for a selection. There's nothing there, though, that remotely looks like the Budweiser B. If all you need is a clean version of the logo, though, go to Brands of the World. You can also do a search there for Budweiser and find a lot of Bud logos.

(And Miller ones, too!)

Just found Brewmaster Modern: a font created to look like the Budweiser script. It may be useful to you.