What means to gum the bullet?

I do not know.

But an expression I know that is somewhat similar is "Bite the bullet"

This means to withstand the pain, endure, accept that there are difficulties, suffer the consequences, etc.

The expression come from a century or more ago when there were no anesthetics available. An injured person would be told to bite down on something fairly hard but not brittle (the lead of a bullet) in order to withstand the pain of surgery.