FCP does not provide finer control of bit rate, but it seems to export in rather high bit rate.
Unless you find that the result is not satisfactory, there is no reason to worry much about getting a higher bit rate.
It really depends on the content, but higher bit rate does not necessarily mean higher quality.
If you are not satisfied with the result, you may try exporting in ProRes, and then use either Compressor or HandBrake to make an H264, with perhaps higher bit rate, but I don't think it is worth the trouble.
Can you elaborate on why you are so concerned with bit rate?