Can I replace a single pole light switch with a GFCI switch combo?
No. With just what you have now it is 100% impossible. 
Right now you have a switch loop which is just a constant hot and a switched hot. Even though one wire is white there is NO neutral in this box, both are being used as hots.

You could run a new cable to this box, but you best bet BY FAR is to have a circuit run to a new GFI receptacle and just leave the existing switch alone. This is almost certainly the only code legal way to go as well. Adding a new receptacle to an existing lighting circuit in a bathroom would not meet code and will almost certainly be inconvenient due to circuit overloading.