I'm using ffprobe right now but I don't if it supports showing whether the video contains b-frames and what could be the syntax. Can I do this with ffprobe and so, how, or is there any other free alternative that could do this?
I found a way. With ffprobe:
ffprobe -show_frames videofilename.mp4 > outputfile.txt
Then you just look for the pict_type entries, which will be either I, P, or B. B denotes a b-frame.