Doesn't sound quite right. You should be doing a little better than that. As always, make sure you're running the latest ATI drivers. With my GTX 470 (which is faster than the 5850 granted) I play Multiplayer BC2 @ 1920x1080 with DX10/11 mode, 4xAA/AF if I recall correctly, and all High settings @ 59/60FPS fairly consistently (using Fraps).
Bad Company 2 can also become CPU bound however. Here's what I'd suggest. Lower your graphic settings (resolution, or other settings) and see if your FPS improves. If it does, then you have a GPU limitation. However, if reducing your resolution does not show FPS gains then your CPU could be limiting your GPU performance. In that case you'd want to overclock your CPU to gain more performance. Bad Company 2 likes quad core CPUs, so you're in a good situation there. But more CPU speed is always good.
You could also use a program to monitor your GPU load while playing Bad Company 2 and see if it ever hits 90-100% load. If it's not, that could also implicate a bottleneck of some type (whether it be CPU or lack of RAM).
You may also want to consider installing 4GB or more of RAM. That's what's needed for smooth gaming these days. Especially if using Vista or Windows 7.