I'm just guessing based on highlighter theory.
Make sure the marker is dry at the tip and not wet. Practice putting down a strip quickly on scrap paper, but not so quickly you might lose control and have to do part of it over. (Identify where your mark is going to end before you start marking.) Then try it in an inconspicuous place in your Bible. There's presumably pages at the beginning or end with the same kind of paper as the interior. You can then see how much bleed through you're actually going to get.
If all else fails, a pencil underline might work for you. Use a regular or harder lead to minimize the amount of transfer to the facing page. Soft lead will smudge if you brush against it. The lead (actually, graphite) will outlive the Bible and can be erased if necessary by a high quality eraser (e.g., Staedtler Mars), but pencil will not stand out like highlighter does.
Colored pencils work, although as with all pencils and pens, put a hard surface under the page. It's inconvenient to carry a slab of marble around and try to fit it under a page, so you may have to experiment a bit. You could try a sheet or two of transparency plastic. A crafts store would have some soft of flexible plastic that can be stored in your Bible, or you might cut a piece out of some plastic container you already have that is slated for the recycle bin. (Sand or somehow smooth the corners and edges so it won't accidentally bite into a page.)