you could always just wear your boots...
otherwise i've packed one bag w/ boots, helmet, goggles, gloves & misc stuff and carried my board.
here, it's possible to get to all three mountains via public transit + shuttle bus or tram, but it's quite the journey vs. driving... as it'd go: bus, train, seabus (ferry), bus or private shuttle bus (with board racks on the sides), & for one mountain a huge tram/gondola.
the other option is taking public transportation buses as close to the base of your chosen mountain as possible and then hitch hiking. people are usually pretty cool about it, considering it's pretty obvious that with all the gear you're intending on snowboarding and not car jacking someone on a road that only goes to the lifts.