I have an Activity
where I have a background image in an ImageView, and nine transparent buttons on top of the image.
http://i.stack.imgur.com/GGQqd.png
That bitmap is huge. The 500k you mention is the compressed size. Images are uncompressed in memory when you use them. You're actually looking at 2048×1536×4 = 12582912 = over 12MB of memory use.
If you're on a device like Nexus 9 that has that screen resolution, then you can reasonably assume it also has the memory, GPU and bus bandwidth to deal with an image of that size. However, if you're on a lower resolution device (most devices are, keep in mind that even Full HD is just 65% as large), then this image is phenomenally wasteful of memory. You can buy low end devices today with a 240x320 screen, where a full screen bitmap is a mere 2.5% the size of your image.
You're going to have to scale that image when you load it. Use BitmapFactory.Options
to set the desired size before loading the image.
Furthermore, you're putting text directly on top of it. Text rendering requires alpha transparency, which requires sampling the underlying image. If you can put the text on an opaque background and put that on top, you'll save some GPU load as well, but I'm actually not sure how much performance that's going to get you. It may not be so big a deal.