I don't mean zooming in. I mean scaling the current zoom level to make
it readable on high-resolution devices.
This is just not a distinction that exists in reality.
What you're describing is basically a texture, so I will use the word 'texture' instead of 'bitmap'.
At any zoom level, a set amount of screen pixels get mapped to a particular real world area in meters. This is your map scale or "zoom level" - the thing in the corner of any map. For example, 10 pixels = 1km.
Your image has an area which it represents, say a 1km square in London, and a size in pixels, say 40x40.
When the software tries to draw your texture to the screen it needs to map the pixels of your texture to screen pixels. In our example, our zoom level is 10 pixels = 1km, so a 1km square on screen is 10x10 pixels. Our texture also represents a 1km square but has more pixels (40x40).
Because these values are different, we need to somehow make our texture smaller. This is called texture filtering, and can also be done to make a texture larger.
The reason your texture looks bad on a high-resolution device is down to how the filtering is behaving. You may be able to achieve acceptable results if you use some kind of mipmap, reducing the level of detail as the user zooms out. This would be analogous to how Google maps removes labels as you get further out.
You will never be able to see a high level of detail from a high zoom level. That's why the answer saying "just zoom in!" are technically right.
If you simply increase the area the texture applies to without equally scaling (zooming) the map, your texture and underlying map will get out of sync and that's definitely not desirable.