There is no ideal size, as it depends on which version of Operating System you want to work (Android / iOs ... etc ..) Although you can see this information: http://stackoverflow.com/questions/34456945/what-size-has-a-background-image-to-have https://developer.android.com/guide/practices/screens_support.html (Page to the end)
Although to create an optimized game, it is not recommended to use such large images, it is much better to create very small, single color and then scale. For example, if you want a green background, you can create a 24x24px image and it will not occupy anything in memory.
For solid colors, I recommend 32x32px For degraded colors, I recommend 256x32px Import to BB and re-scale to 10, 20 or 30.
Hi I have seen this often so I'm curious, what's with the number 32? Why don`t you use 1x1 pixel images for solid colors?
I started making games with Game Maker, and in the tutorials it was indicated that it was better to use the resolution, 32x32, 64x64 or 128x128 for the characters. I think it is so that the character does not occupy the entire screen, there are videos or tutorials of BB indicating that the character of a game does not have to be very large. I use 32x32 for solid colors, because they do not take up much space, and when I add them to a scene, I can handle them correctly at first. I do not know if BB can handle objects of less than 32x32 (1x1) or if there is a problem, but that resolution works for me.