Going out with someone doesn't change our sexual orientation. We stay bisexual.
And we can go out with someone, be monogamous, and STILL be proud of being bisexual.

Being bisexual = being bisexual
Being bisexual =/= being automatically available for a relationship (sexual or romantic)
Being bisexual =/= wanting to have sex and/or have a relationship with several people at once (there's nothing wrong with that to be clear when everyone involved is up to it, but it has NOTHING to do with sexual orientation)

Being bisexual = being bisexual