If I needed to do that, I'd probably draw the bitmap and the caption text using SVG in a single "image", and then use the usual techniques for scaling the SVG image up to the size of the screen.
Caveat: With this approach, you probably must include at least one embedded font and use it for all your captions if you want the rendering to be even halfway consistent across readers. I mean, there are ways to embed arbitrary blobs of HTML in SVG, which could in theory allow you to let the reader determine the sizing and style, but IIRC, that feature isn't very well supported.
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