I don't believe there is any further warning. I'm pretty sure it starts its own little 'fuel/trip odometer' to show you how far you've travelled with low fuel warning on.
The above post is pretty accurate for judging when you really need to fill up.
You can also judge by how much fuel the bike takes to fill up afterwards.
Correct, there are no other warnings aside from the last flashing bar and the F-trip counting how many miles you have traveled since the warning first began.
Some have pushed it into the 50+ miles, but that is WAY too low. It's not good to run it that low. Filling up around 35-40 is fine.