Should I ditch my mage?

If you really want to be asked to come to bosses (rather than begging the host that you can tag along) then you probably should switch job...

All characters can get into boss runs, not all of them are there because they do anything useful.

Also it brings up the point that even if you're gMS' most powerful hero/NL/BM/whatever, you're not guaranteed to find boss runs. You still need to know the right people who will let you come along.

Of course, being things like bishops/DKs, you have a higher chance of being able to going with strangers. Still doesn't guarantee though.