Have you checked if their is a Federal Govt. policy on bike parking. Covered secure parking is what I would expect in Govt buildings up here. It's not unheard of for local management to be unaware of such policies or ignoring them.

If exterior parking is the only option, I'd ride the good bike when the weather was good and the old bike in rain or worse. I'd leave a heavy chain or heavy U lock attached to the bike rack to secure whichever bike I rode and carry something lighter for stops enroute to pick up groceries etc.. I'd also carry a shower cap to cover the seat when it was raining or likely to do so. I'd also replace all quick releases.