The how long is a piece of string answer - but then you probably knew that, didn't you.
The length of thread on the bobbin will depend on how thick or fine the thread is and how tightly or not your machine winds it.
The bobbins that you use for the needles will be used up at more or less the same rate. If you use a similarly filled bobbin for the chain looper thread, it will be used up much faster.
How much faster will depend on whether you're stitching a wide or narrow coverstitch and also what stitch length you use. A shorter stitch length will use up more of the looper thread than would be used over the same distance with a longer stitch length.
A useful tip is to use the cone or large reel of thread on the looper and the bobbins on the needle thread.
Alternatively, if you're not too worried about seeing the looper thread on the inside, use a cone of a base neutral thread for the looper and the coloured threads on the needles. An overlocker thread, or one of the fine polyester monofilament type threads will do for the chain looper for coverstitch. It doesn't need to be a heavier sew-all thread unless you particularly want to use it.
3 shades of base neutral are often sufficient, eg. off white/cream, light grey and darker grey tend to work with most colours.
If you want to use the serpentine side of the coverstitch on the public side for a decorative purpose, then using sew-all, decorative threads or thicker/heavier threads are used in the looper.