I wouldn't encourage you to wait until he gets used to it. The process is very stressful and goes against the nature of your betta.
It might also lead to tailbitting and many other related problems.
I don't have backgrounds in my tanks and I like it that way because I'm not putting my fish under stress, it's just the white wall behind the tanks.
You've created this perfect home for your bettas where he feels comfortable and secure but then it's invaded by this other fish that does not go away and wants to fight him all the time... this is how I've always seen it.
Try to use a different background that doesn't create a reflection.