If this bike is going to be out of your sight at any time, make sure you're using 2 u-locks (front wheel to frame, frame/rear wheel to immoveable object). Bike theft in L.A. is becoming absurd.

Also make sure that your building is OK with you bringing the bike TO your office.

If I were you, I'd pick up a used bike off of Craigslist (like, say, this $300 Benotto -http://losangeles.craigslist.org/sgv/bik/1559247532.html), and see how you like commuting by bike and how easy it is to store your bike, etc. If you don't like it, you can easily resell it for close to the purchase price, and if you do like it, it's always nice to have a spare bike.