Fix your good bike and ride that. A truing stand, spoke wrench and spokes will cost you $50-60. Heck you could probably get by without a truing stand and save $40. Sit down and spend a couple hours learning how to true a wheel. That is IF your broken wheel is repairable. If it isn't, you can find fairly cheap wheels. I outfitted my bike with a wheelset that cost around $100. I've seen sets for around $80. If all you need is one tire, you can get it even cheaper than that (there's also craigslist).
So if you fixed your bike and skipped the bus for a month, it would probably be a wash in terms of cash. Anything after that, throw the $3 you save every day not taking the bus into a high-interest savings account and watch it grow. $60 a month can grow pretty quickly.
Take a change of clothes to work and a towel. Many many people face the same challenges you face and still manage to bike every day. Save the bus for those really rare occasions where you can't ride.