I know I'm just re-iterating what others have helpfully said already, but I too, suggest trying lowering your recording settings and/or your game settings, to see if this helps you.
I just tested CS:GO with Bandicam 2.2.0, using various codecs (Xvid, Third Party x264 [the slowest out of these but it can look really good with the right settings], AMDAPP, etc) and my FPS did drop down to 100fps, but that isn't bad [in my mind]. Are you trying to record at a constant 120fps at 1080p or something? I just upgraded recently to an AMD FX-8350 CPU and AMD Radeon R9 280 GPU, which made a huge difference (games run so much smoother now!) and lessened the 'performance hit' of recording a lot for me... The others are right, perhaps it is just a bit much for your system at this point in time.
Have you tried other codecs, like MJPEG? It is a more 'lightweight' codec, that uses less processing than most others (even though the VBR Quality must be set higher to keep comparative visual Quality, in my opinion).
Were previous versions of Bandicam working for you? In the past, I found a version of Bandicam that had a large hit to the performance for me, and working with Bandisoft, they were able to fix the issue in the next version of Bandicam that came out (this was around 1.9.2, if I remember correctly). If you really can't get it working with this version, try downloading past versions of Bandicam at their Softonic downloading area and see if an older version works better for your hardware. If it does, let them know! Perhaps there is something there, too... Edit:
I was able to do some quick testing, so just wanted to pop back in to say that I did some testing with other Game Recording Programs I had...
FRAPS (bought long ago) brought my fps in CS:GO down to about 80fps from about 150fps
DXTORY (friend bought it for me a while back) brought my fps down to about 80 as well (Dxtory Codec)
BANDICAM brought it down to about 100fps from about 150fps (Xvid/avi and MPEG4/mp4 codecs)
These numbers are what was showing while recording and playing CS:GO
The actual captured fps (target:60) was below 60fps if I wasn't recording to my SSD (down to about 40 on an old slow HDD). It maintained the target 60fps on the SSDrive.
Just a comparison to show that Bandicam doesn't seem to be much worse (in fact is slightly better in capturing performance than those other non-free programs, in these tests it seems). These were all tested on the same system, with the same settings.
Bandicam does a lot of compression on-the-fly with many of the codecs, which is CPU-intensive, depending on which codec and settings you choose. I went from a 4-core CPU to an 8-core CPU and found that the performance hit when recording with Bandicam went way down! Try to lower the recording settings and also try lowering your in-game settings, to find out what affects it more...
Whatever is causing this problem for you, I hope you figure out what it is - don't forget to try older versions too, maybe something has changed and finding out what it is may help you, too.
Good luck with it!