You should probably hope your DM realizes that Bards can already take as many Multiclass feats as they want, because that's one of their class features, and also that Songblades can be used as an implement for Bard powers as part of their item description.

Well, or just tell him...

Anyway, multiclassing into Swordmage as a Bard can be fun and profitable as long as you've got the INT. More of a Cunning Bard thing, but it'll probably still be good. A Songblade is a blade, so it counts as a Swordmage implement.

Which means you can just take the MC Swordmage feat, and you're practically all set!