@OP: Your bitmap approach (literally, bit-as-in-boolean map, not as in graphical texture) is a perfectly fine approach. Your mouse-cursor will be within the bounding rectangle of only a handful of regions at a time in a vast majority of situations, and you can easily quickly test if the cursor is over an activated bit for one of those very easily.
One gotcha is aliasing; if your player can zoom their view in any way, one mouse-cursor position might round to hitting several regions at a time, so be sure there is a predictable order of resolution (e.g. sort states by ID, always pick the north-east most, etc), to prevent possible odd behaviour when the player points at or near a border while zoomed out.
RIP GameDev.net: launched 2 unusably-broken forum engines in as many years, and now has ceased operating as a forum at all, happy to remain naught but an advertising platform with an attached social media presense, headed by a staff who by their own admission have no idea what their userbase wants or expects.Here's to the good times; shame they exist in the past.