Been through this with my cars as well, but haven't tried coming to the point where the single bar starts to flash. Was curious as to what starts flashing and as to what the signs look like.
Off-topic:
Don't know how true this is but I've heard that testing with low fuel can put strain on the fuel pump.
That's actually true. It's generally considered a bad idea to run a fuel injected bike (or car) to empty... do it enough and you'll be paying to have the fuel pump replaced. With the fuel pump being submerged in fuel, it relies on the fuel itself to cool the pump during operation. Even running an EFI vehicle to a very low fuel level repeatedly can cause the pump to fail prematurely, due to it overheating. Not to mention some EFI vehicles can be a ***** to restart after running out of fuel.
Just like the CBR250R, Honda purposely calibrated the fuel gauge on the 300R & 300F so that when the last bar starts flashing, there would be plenty of fuel left in the tank to both get the bike to a gas station and keep the fuel pump submerged in gas.
Unless you find yourself really out in the middle of nowhere when the last bar starts flashing, you should have no problem being able to ride for another 25 - 30 miles to get to the next gas station, while still having enough gas to keep the fuel pump submerged. The fuel pumps for these bikes are over $200 USD, so overheating the pump is probably something you'll want to avoid over the long haul.
I can't remember the last time I saw the last bar flashing on my 250R, as I typically refuel when it gets down to two bars remaining on the gauge and around 150 miles elapsed on the tripmeter, which then takes about 2 gallons to refill the tank. Once I went as far as 230 miles on a full tank, but that was really pushing the limit as far as how much gas was left in the tank for the fuel pump cooling... as I recall, it took 3 gallons to refuel after that 230 mile run. I'm typically getting 70 to 75 MPG on my CBR250R.