Actually you can polymorph both yourself and your paladin steed with the same spell. It's that perk of Find Steed - when mounted you can make any spell that affects you also affect your paladin mount. As for cantrip trickery, Magic Initiate and Spell Sniper can give you cantrips from 2 classes in addition to your own if you feel like it, although that's probably a waste of feats.
Also, yeah, helping yourself to all the cross-class spell combos in the game is one of the hidden strengths of playing a Bard in 5E. That and extremely high initiative and dispels (at least if you're playing a Lore Bard).