I would be a little suspicious of that 1.011, especially if as you say the sample is very fizzy.
When the beer is gassy little bubbles tend to form on and stick to the hydrometer and lift it up a bit giving what's called a False High reading.
Depending on what else went into the brew, The FG would normally be around 1.008-1.010 sometimes even a bit lower.
Take a couple of hundred mL of beer into a glass, pour the beer back and forward between a couple of glasses, this will stir and warm it up, booting out any excess CO2. When the beer stops foaming take your reading.
Wait a day or two, do the same again, if no change its safe to bottle.
The other thing to look for is the bulk of the yeast having settled. I used to do a lot of my brewing in 23L glass carboys. When the beer was clear enough to see your fingerprint on the other side of the bottle - through the beer, the beer is what is called Cask Clear and ready to bottle.
This happens when the yeast gets below 10,000cells/mL so plenty to give your beer condition, but no big slab on the bottom of the bottle, you get nice clean beer with little sediment, the yeast in the bottle tends to be young yeast so it isn't as prone to breaking down and producing off flavour's.
Mark
