The key to tackling these kind of positions in a game is to imagine where you would like to put your pieces and then see how you could achieve that.
In this position for white the first aim would be to get the king to e5 to attack the e6 weakness and at the same time threaten to infiltrate on either f6 or d6. The problem is that black will have no problem defending the e6 weakness and defending the infiltration by keeping the king on e7 meanwhile shuffling the bishop.
Another weakness will be required to make progress. As it happens there is also no way of getting the king to e5 while the f pawn is on f4 so any plan will have to start with sacrificing the f4 pawn.
If it were white to move then the immediate f5 would force open the g file, a second weakness. Black would have to accept the sacrifice and ef would expose the black king to check from the rook so gf is forced. Then there is no way for black to both prevent the rook penetrating on the g file and prevent the king from infiltrating via f6 or d6. One line could go like this:
[fen "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 w - - 0 1"]
1. f5 gxf5 2. Kf4 Be8 (2...Kf6 3. Rg3 {and black can't prevent the rook coming to g7 next move}) 3. Rg3 Bg6 4. Ke5 {Black is in zugzwang. Either the white rook is going to penetrate on the g file or the king is going to infiltrate on f6 or d6}
So, black's first task is to stop this simple plan. The only way to do that is with Kf7 which unpins the e pawn and allows the recapture ef. The problem for white with this is that it gets rid of the weak e6 pawn and replaces it with a weak d5 pawn.
The now open e file is nothing like as good as the open g file because of the white pawn on h6. The only way for black to defend an open g file is to block the file with the bishop on g6 but for the open e file all black needs to do is to cover the entry squares of e6, e7, e8 which can be done either by the king on f7 or a combination of the king on f6 and the bishop on c6. The weak d5 pawn can be protected by the bishop on either c6 or b7 and the white king can be prevented from infiltrating via e5 by the black king on f6.
If white could both threaten to infiltrate with the king to e5 and threaten to take the d5 pawn with the rook then a zugzwang could be possible but unfortunately the only way for the rook to threaten the d5 pawn is from e5 and if the rook is on e5 then the white king can't go to e5. Hence this position is a fortress.
This is what the lines would look like:
[fen "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 b - - 0 1"]
1...Kf7 2. f5 exf5 3. Re5 Bb7 4. Kf4 (4. Re1 Bc6 5. Re2 Bd7 6. Kf4 Kf6) Bc6 5. Re1 Kf6 6. Re2 Bd7 7. Re5 Bc6
Going back to the initial position is there anything white can do to prepare the f5 push to make it work? Or, to put it another way, what must black do to stop f5 from working. The answer is that black must keep the king on f7, ready to both defend the e file if it opens and to play kf6 if white threatens to play Ke5. At the same time black's bishop must defend the d5 pawn from either c6 or b7 whenever the white rook is on e5 and it must defend the e8 entry square from d7 or c6 whenever the rook is not on e5.
