Are there any rules against putting an exhaust fan above the bathtub/shower itself?
The fan would have to be listed for wet locations.
Actually, it only needs to be damp rated if it is not subject to shower spray. The commone NUT ONE exhaust fan is so rated provided you feed it with a GFCI.
Exhaust fans with a UL listing for installation over a tub or shower on a GFCI circuit can be installed over a tub or in a shower. This applies to most exhaust fans with light. Units that include any type of heating function to them are not able to be installed over a tub or shower.
Here is a link that might be useful: Chandeliers Brisbane