What do I do when my opponent plays the bowlder attack well

Normally, I'm pretty happy to see the bowlder attack. But I ran into an opponent who played like this against me, and though I won in the end, I felt pretty passive in the early stages. Both my normal pawn breaks were stopped, and generating activity was pretty difficult. Nf6 is met by e5 with no good squares for the knight. (I ended up playing b6.) Is there a better way to play against this? 

• When you're opponent plays the "Bowdler Attack" you thank them. It's a silly choice by white. You don't need to waste time with a6, I don't think. White is allowing you free development of your knights. Play Nc6, since white has already shown they won't attack it with Bb5, then Nf6, then punch through d5 with tempo. Your center is much better and your development is at least equal and white is left to think about what a stupid opening they played. They're probably best to transpose into a tempo down open Sicilian.

Actually, now that I think about it Nc6 seems good, because if Nf3 (Trying to allow white to push e5) I can play Nf6 with the idea of Ng4 in response to e5 where black wouldn't be able to defend the pawn. If they don't play e5 I can slam d4

(Btw my idea behind a6 wasn't to stop Bb5, but rather to threaten to push b5. I still think it might be decent here since it can be played with tempo as white needs to respond, and does stop annoyances with Nb5 that might happen later.)

Thank you for your response though, it helped me.

The Bowler is considered bad, as the Bishop will be kicked via a6 and b5 and c5 or e6 and d5, it is played by people who do not know how to play against the Sicilian correctly. However, I myself and many others found it very annoying to face for a while, but my strategy is just to play e6, Nf6, and d5 and you have good space in the center with your pawns.  

I feel like you may not have fully read my post, since I was mostly asking about when my opponent tries to prevent those ideas, as in the original diagram

Why do you play a6? I'm not sure if that is book, but I usually go along with my plan with controlling the center with Nf6.

The idea of a6 was the threaten b5, and also to stop any Nb5 ideas later if I put my queen on c7. It seems like a good move since it doesn't lose any time, as black has to respond with a4. Nf6 to early seems to run into e5 where the knight has nowhere to go

I see.