You are going to have to go inside of the transceiver unit and crank the modulation up to 100%. You can be certain it's not even close to 100% stock. I don't know who made the radio for Honda, but someone did, so a schematic is out there somewhere for it. Turning the modulation up will help, but probably only a little. The audio quality from whatever mic you're using could also be upgraded, but that is aminor attempt at a major mod for what you'll get in terms of ability in being heard better. Because of the crappiness of that particular band, CB'ers are always wanting to hear something better than most stock radios and their muddled microphones.
As far as running more power, first tune what you've got... All radios can have their transmitter sections aligned and peak tuned for output. Then there is the tuning of the antenna to get that power out over the air. Your coax connection between the radio and the antenna plays a major part in that too. Adding grounds to the coax outer shield on both ends will help the antenna see a better ground. A ground from the antenna bracket at the base of the antenna will help also. Grounding of the antenna "system" is important in any mobile app., especially on a bike that is too small a footprint anyway for that band. Tune the antenna as close to a nil SWR reading as possible once your grounds are the best you can get them.
Running a small 50-100 watt linear amp will help you get out, but you may end up talking further than you can hear if the above is stuff is not done first. Running more power than that is a waste of money and too taxing on your electrical system IMO. Small 50/75/100 amps can be had that will fit in a standard Cobra 29 sized case replacing the speaker, so finding a spot on your bike for it should be easy enough. You'll have to mount it in a small RF/weather sealed box, which are a dime-a-dozen on the net.
Lastly, any competent radioman can work on the radio, but make sure it's not some CB hack that thinks he knows something about radios. There's a lot of screwdrivers out there tearing-up some radios with less than adequate skillsets calling themselves a"Radioman". CB'er hacks are way too abundant, and a legit Radioman probably won't touch it unless you know him.
Just throwing a amp on a poorly tuned set-up may get you what your looking for, but it would be like riding your bike while it's running on 3 cylinders.
Tune what you got first...