To get this your Online Career race has to be broadcast live on Gotham TV.
The easiest way to do this now (mid 2009) seems to be by racing the ranked Gotham Duelling.
The biggest problems with racing ranked in 2009 is the lack of people still playing the game combined with the rather flaky matchmaking system. However, Saturday mornings (GMT) seem to be your best bet. I've run about ten "Gotham Duels" over the last two days and been on Gotham TV six times. Friday morning took me an hour or so to get a single race, Saturday morning just a couple of minutes.
I would recommend leaving a "preferred" player feedback for anybody you do find to race as this improves your chances of being matched with them again if you are going for "Online Professional".
Edit: According to comments below it would seem the servers have now been closed down making this impossible to get hence forth. Thanks to Optimus Doug for pointing this out.