I like Knotted's suggestion, or maybe it would be easier to fit a run in with the ride to work if you rode to work first, and did your run near your office? You may find that the traffic is lighter a little earlier so you actually shave some time off of your commute, and I'd bet you'll ride faster thinking of your run than of work.

For the days when you want to do yoga or meet your friend at the pool maybe you can take your bike on public transport or get a ride from a co-worker that lives near where you are going? (since you're in Utah maybe you can even find one with a bike rack? )

You can do it.

Anne