How can I remove this stuck screw in my bathroom?
I like the approach of going in from the front offered by dandavis. But, you have some others. First, it bears mentioning that you should duct tape a piece of thin sheet metal you have handy out from the set screw to protect the surface. 

Before we begin, did you try some Kroil and a larger key first? It could be it's reluctant because the threads are slightly corroded. I think trying to use a binary epoxy to spin it out is likely to fail.

Some other options depending  are:


Use a flexible shaft to hold your bit.  
Use an extended drill bit.  
Instead of a grinder, use a cut-off wheel on a
grinder or cut-off tool. This way you're slicing through what you
need to. It's tough to determine what the dimensions are, but if you have a 3" wheel, you should be able to get rid of that set screw without many issues.


Good luck!