Isn't the Bogo-Indian just busted with this line? I know openings often tend not to be busted, and I'm obviously not really suggesting that the Bogo is busted. But I recently played a Bogo-Indian where I just couldn't find any follow up quite early in the game and my moves just looked natural...

I also just don't understand that white's 9.e4 move in the diagram has never been played in the database but shows +1 advantage...

Maybe some help on how black should approach those lines? (By the way, I'm new to that opening)

[FEN ""]

1. d4 Nf6 2. c4 e6 3. Nf3 Bb4+ 4. Bd2 a5 5. a3 Bxd2+ 6. Qxd2 d6 7. Nc3 Nbd7!?
(7... O-O) 8. Rd1 b6 9. e4! {I can't understand why this move hasn't been played
before, but engine already gives quite the advantage to white...} 9... Bb7 10.
Qc2 Qe7 {Getting away from the d1 rook but not sure how solid it is} 11. Be2 O-O
12. O-O {ok now what? Already a bit lost on what to do,  played the following
move to claim myself some space but it just gave white a big hole to look for on
b5 and weak b6} 12... c5?! (12... h6 {engine, but can't see what this does})
(12... Rfe8 {also engine}) 13. d5 exd5 14. cxd5! Rfe8 15. Nd2! *
Well, the Bogo-Indian as an opening is hardly busted, but the way black played that opening, there is no doubt that white has a huge advantage in the final position.

The main reasons that black gives up the dark-squared bishop are not to lose time, but then, and this is more important, because he can regain some dark-square control by placing the pawns on d6 and e5, and pressure e4. Often the Nd7 can also find a very nice home on c5 since a5 has been played.

The way it was played in that game, black never did that, and black did not even attempt to contest the center. It was a recipe for disaster. The final straw was exposing the huge hole that was created on b5.

 [FEN ""]

 1. d4 Nf6 2. c4 e6 3. Nf3 Bb4+ 4. Bd2 a5 5. a3 Bxd2+ 6. Qxd2 d6 7. Nc3 Nbd7 (7... O-O {The most common move here.} 8. g3 Nbd7 9. Bg2 e5 $14 {Is a main line. } 10. O-O exd4 11. Nxd4 a4 {Securing c5 for the Nd7.}) 8. Rd1 (8. e4 {Why not this immediately? This is the main move.}) 8... b6?! {This is not necessary here, and we are not even sure that the bishop will go on b7, which I tend to doubt...it may come to g4 and trade for a Nf3 even. It also ruled out a later c6, which would have been desirable later after e5.} (8... Qe7 {This is more natural here, aiming again for e5, and removing the Qd8 from the same line as the Rd1 and Qd2 battery.}) 9. e4 Bb7 10. Qc2 (10. Bd3 {Finish development is more natural here, and later if the black king castles short, then the Bd3 will be aimed at right it.}) 10... Qe7 11. Be2 O-O 12. O-O c5? {This just looks wrong. You still want e5, and if d5, then you have Nc5 and a4 solidifying the Nc5's position. Also, this shows how dead the bishop is on b7} 13. d5 exd5 $2 {This natural move really secures white's advantage because the hole at b5 becomes palpable.} 14. cxd5 Rfe8 15. Nd2 $16 {White almost has a significant, and almost winning, advantage.}