Meriah,
Unfortunatly letting him cry and then giving in after 45 minutes is really going to bite you in the behind. The next time you do it, he will cry much longer, because he expects that you will give in eventually.
It is NOT easy but, somehow muster up the love and compassion to help him. I know he may not be receptive to it, but try to rock him, or read to him quietly, or play quietly with the lights low. Yes he will probably scream, BUT if you want to break the habit and avoid tooth decay issues due to this....then that is what it may take.
I am sure there are games, etc...you can try and play. But at 15 months old, my kids didn't have the longterm memory or ability to reason for any of that to work.
We broke my son of his pacifier at about the same age, and he screamed for two nights and then he would cuddle in to sleep with no problems. We cuddled him, spoke softly to him, rocked with him, etc... So he knew we loved him, but did NOT give in. Once he figured it out, he was wonderful.
He may eventually give it up on his own, but he may not. I am not saying what you should do. If you want to stop the night time bottle this is what we did. But if you don't, then don't. No matter what, he won't be in school with a bottle, etc... :-)
Blessings.
M.