Any ideas how to replace bulb in this bathroom ceiling fan

Might be clips around the perimeter. Try running a butter knife or some kind of shim around the outside to see if you hit anything: if you do try poking in on it.

You can easily run an exhaust fan through a window opening. Look at all the window mounted air conditioners. Same concept without the cooling capability. The main constraints are cost and appearance. As you can imagine, the more handsome the installation, the more it will cost. You basically will want to use a small square duct fan, similar to a very small box fan or very large computer fan. You should consider at least a short duct so you can incorporate a backdraft damper to minimize infiltration when the fan is not in use. You may also want a louvered grille for appearance or privacy reasons. Depending on how this is accomplished, the exterior decorative bars may need to be reworked slightly.

It sounds like this window is in or above the shower itself. In such a case, all electrical work will need to be approved for wet locations (I believe if above 72" from floor, only damp location measures are required, but please verify this). The simplest installation would be to open the window, run the duct through the opening and close off the remaining opening with an insulated panel of some sort. The sliding panes will need to be fixed in place somehow for security. Fan wiring can be run in surface mounted EMT tubing.

A better solution is to remove the wood window, which is not the best material for wet locations. Install the fan/duct and some minimal infill framing in the rough opening. Any wood in contact with masonry should be pressure treated. Install a new PVC window in the new, smaller opening, with obscure glass. A cleaner look will be achieved if you can hide the fan wiring behind finished surfaces. Depending on existing conditions, this can be somewhat simple or quite expensive.

A glass brick solution is also possible. Depending on the size of your opening and the brick module size, it may be an excellent or poor solution. Ideally, you may need no infill panel at all, the duct may fit nicely in one corner. Or so much infill is needed that the glass brick solution is just too visually insubstantial to be worth doing at all.