You played a good game really, the opening was kinda wonky though (is that a word lol).
I've come to realize that many mistakes for any level stem from having these bad tapes stuck on repeat in our heads. For example once we decide a certain pawn break or outpost or piece is strong, we can continue to think so even long after the situation has changed. In this game your bad tape was that diagonal for your bishop :)
You say you want the bishop on a good diagonal for when the position opens up, great! But when and how it opens up is decided by the players, don't count on it as an inevitability that your bishop will be well posted. Fight for your ideas!
So for example on move 6 consider the move d5. He may lock it up with e5 but you have space and he has made passive moves. Forget about your beautiful bishop (it was never guaranteed to you) and play with your new pluses (space and development).
6. h3 Another bad tape so to speak. The strongest position for your king really really is to have moved no pawns. Plus black has made many passive moves, no need to shore up the g4 square. Finally, this move is too slow for the opening phase unless it addresses an immediate problem.
7.Bd2 -- e4 isn't under attack. Bd2 is a passive square. Better is 0-0 and Re1 if you're worried about e4.
9.Bb3. The bishop, as they say, is biting on granite. Bd3 was better, the a2-g8 diagonal is not useful in this position for white.
10.bxc3 d4 doesn't need to be defended immediately, so consider taking a few moves to defend it with the c pawn. For example imagine something like this.
11.a3 and you're still stuck on the wrong idea, the bishop doesn't belong there and this move is too passive for the opening phase. 11.c4 works on your "problems" i.e. the doubled pawns, and freeing the bishop.
14.e5 The queen's diagonal was not an issue here, and neither player is aiming to make use of f5 or d5. Locking up the position lets black off the hook for his passive moves. This was a perfect time to play c4 and work on your "problems" again.
If your bishop had been on d3, you would probably have great attacking chances though (after e5 that is). In the game though, it solved more problems for black than it did anything for you. Anyway, check this fantasy position out, which side would you rather be playing?
And actually, in the game position, you can consider 14.d5 to open things up as you're ahead in development. The only downside is your doubled pawns can immediately come under pressure.
15.Bxh6 Great move. I like black's response too, very much to the point.
As recommended by the chess.com staff, I didn't use a computer to analyze this 15 10 Live Chess game. After opening with 1.e4, I commented on all of my moves, along with my thought process during the game, and in those annotations are questions. One big question is: what did I do wrong to have my light square bishop completely shut out of the game?!
Answers to my questions, as well as any ideas on how I could have played better in general, are greatly appreciated! Thank you.