The most compact bag for what you want is the TT Glass Limo. TT Glass Taxi for hood reversed. Both should allow TCs to be attached if required. For carrying more gear along side the best I've found are Gura Gear Bataflae series. 32L will fit the hood extended and body on one side and then an entire other side for tonnes more gear. 26L will fit the hood reversed. 18L will fit without body attached and hood reversed.
I also own the Tamrac bag some have mentioned but that is my 600II bag with body attached and hood reversed. I haven't used it yet with my 300II (I just got my 300II two weeks ago) but it would definitely swallow up the full thing hood extended.
Also as for the postings about the 300's IQ with TCs. I can speak from 2 weeks of shooting and using both the 1.4 and 2.0 version III TCs on the lens. The IQ is amazing even with the 2.0. I'm sure there is some IQ hit when you look closely but it is still better IQ than my 100-400 at 400. AF with 1.4 doesn't even take a noticeable hit, with the 2.0 it is a little slower to acquire initial lock and if you lose lock then again slower to re-acquire. However, it can easily track birds in flight in AI Servo with no problem. It is better than the 600II with 2.0TC where the AF hit is more noticeable. However, all combos of the 300II and the 600II even with the 2.0TC are better at AF than the 100-400 with the 1.4TC. (This is all on the 1DX).
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1DX / 5DMKIII / 1DMKIV / 7DII / Bower 14 f/2.8 / 17-40 f/4 / 24-70 f/2.8 II / 24-105 f/4 IS / 40 f/2.8 / 70-200 f/2.8 IS II / 100-400 IS II / 200-400 f/4 IS EXT / 300 f/2.8 IS II / 600 f/4 IS II /