How do you spell bye themeselves?

The correct reflexive pronoun is "themselves" -- the plural form of himself or herself (and in some cases, itself and oneself). The term 'theirselves' is a dialectic artifact (as is 'hisself' ) and is not formally correct.

The pronoun theirs and the adjective their are both possessive, and normally would have no 'self' form.

The reflexive pronouns are:

myself

yourself

himself

herself

itself

(oneself)

ourselves

yourselves

themselves

*majestic plural ourself

*gender neutral singular themself