I really prefer my hybrid with fatter tires for commuting. There are a lot of advantages to ahving a "beater" bike for commuting, including that when you get back on the light bike, it's FAST :-) I picked up my Schwinn Racer for $32 on e-bay (plus about that much for shipping, plus about $50 to overhaul it)... it's got about 8,000 more miles on it now.
The only way to get past the "oh, it's not that I don't want to!" stuff is to decide that you want to do it anyway, aiming, say, for *one* trip just to say you did it (to shut people like me up :-)) .
Have a friend who drives who'd let you stick your bike in his/her car? Or... find others who might want to too, pool together to buy a bike rack... or... cruise the whole building...pretend that on X date, well, you *have* to ride the bike (because the car is not available)... and make the necessary arrangements.
There is travel attire designed to help people be sharp and presentable despite challenges...
If you really *do* want to, you just m
ayh be able to find a way.