I just Bought a Sapphire r9 270x , i have the same cpu... I Run battlefield 4 on ulta 8x msaa 40-50 FPS(so i run it with 2x and i get +60fps). There's no bottleneck there, cause is the maximun that r9 270x can handle. Of course the a8 3850 is overclock at 3.6 Ghz(2.9 reference clock) with AMD overdrive, not big deal, but for sure with stock cooler it will overheat to 60-70c°, i have a cooler master evo witch cost $25, so the temperature is 45-50c° maximun.
if don't want to change/buy CPU/Motherboard Combo, yes you can go ahead and buy the r9 270x.
Note: Also at 2.9Ghz there's no bottleneck eighter and of course if you got the money buy a AMD FX 6 or 8 series with a am3+ motherboard
sorry for my english.