As adjectives the difference between bummy and rummy
is that
bummy is (us|informal) like a bum (homeless person or hobo) while
rummy is (dated) peculiar; odd.
As nouns the difference between bummy and rummy
is that
bummy is (childish|slang) bottom; buttocks while
rummy is (uncountable) a card game with many rule variants, conceptually similar to mahjong.