1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O b5 6. Bb3 Na5?!

Black drops a pawn, but is capturing white's better bishop and doubling up white's pawns compensation?

Firstly, the notation-diagram doesn't match. 

Secondly, both of these openings seem playable but I wouldn't recommend giving up your central pawn + opening the a file for white.

Seems to me the diagram does match the notation but at this point, White's king bishop is almost bad (not good) since he has a central pawn on a white square. So, besides giving up a central pawn and opening a file in exchange for a "bad" bishop doesn't seem like a good bargain right now. (Just a patzer's opinion)

My apologies. I made the moves on my board and was looking at that.

Black is not dropping any pawn. If he would , doubling white's pawns and eliminating white's light-squared bishop wouldn't be enough compensation.

There is very little problem with doubled pawns on the queenside wing, it would definitely not be worth giving up a whole pawn for. The Samisch Variation of the Nimzo-Indian allows doubled pawns for what is essentially about one tempo.

Believe it or not, but Black is about equal, or at least slightly better off in the following game, despite not only having doubled pawns but having isolated double pawns.

Black has an open diagonal, meanwhile White has lost one of his main opening weapon: his powerful light-squared bishop whose file he just opened, and the bishop pair. And it's that light squared diagonal Black will now bring his bishop into play again.

In fact this was an old trick people would often play as Black against old computers who would almost automatically double the pawns without considering development properly.