May one chew gum on a fast day?
The authorities debate the question of
whether chewing constitutes “eating”
in the Halachic sense. Hacham Ovadia
Hedaya (1890-1969), in his work Yaskil
Abdi, rules that chewing gum is not
considered “eating,” and thus one does
not recite a Beracha before he chews
gum. Hacham Ovadia Yosef, however, in
his work Yabia Omer (vol. 7, Orah Haim
33), disagrees, and rules that if one
chews gum coated with sugar or other
sweetening agent, he must recite the
Beracha of She’hakol. By the same
token, it would be forbidden to chew
sweet chewing gum on a fast day. One
may, however, chew a substance that
has no flavor, such as wax used by
people wearing braces, as this
certainly does not constitute
“eating.”
http://www.dailyhalacha.com/displayRead.asp?readID=1786
According to the of the Yaskil Abdi where you do not make a Bracha on chewing gum as it is not considered eating then you would be allowed to chew gum in the bathroom.