...will the bass travel very far or will it get lost since there is no containment like in a house...
The bass will actually travel farther than high frequencies. But I know what you mean by "lost" i.e. since it has so much room to expand it will not be concentrated like in a home or in a car which is correct. The walls of one corner of an infinitely large room would "squeeze" the bass into 1/8 of the directionality compared to out on your bike. If I'm recalling correctly, each time you cut the space in half, the pressure doubles, and the SPL goes up 6 dB. So that bicycle will lose 18 dB at -very- low frequencies compared to the room.
Another problem was pointed out in an Audio Engineering Society paper by Louis Fielder who was at Dolby at the time. It is well known that human hearing is insensitive to bass (Google "Fletcher Munson"). He then extended that to say, essentially, "if you can't generate enough SPL at a certain low frequency, then you won't hear it and are wasting your time."
So yeah, on your bike you might as well not bother with low bass.
This actually sounds like a good application for one of those DSP "bass extending" technologies. They operate from another oddity of hearing: you will "hear" the bass fundamental if all the overtones are correct. I think Audyssey ABX is one such system; I just can't remember the others. If you want to pursue that, a different thread is in order. A non-DSP application of that was some tiny KEF 4" woofer speakers which reproduced jazz bass amazingly well, presumably because although the lowest bass notes were not audible, everything else was "right" and the brain filled in the difference.
I'd make your amp with a simple ADJUSTABLE 1st order highpass filter to cut out the very low bass and concentrate the amp power where it is useful. Please note that according to research I did, a steeper filter will NOT improve available amp power although it can reduce excursion. That's because though the filter is less below cutoff, it filters more above cutoff compared to steeper filters.
Don't go nuts and make some 100 Hz ported box, or use a steeper highpass filter. Due to severe corruption in the time domain, you will mess up the overtones and completely lose that "hearing the missing fundamental" effect. Maybe a 60 Hz port in a design with a very shallow slope, but really I would avoid porting in this application.
NOTE: I am using a generator on my wheel and I only make 3W.
Other folks here know better, but for typical amp designs you would need to reduce that down a lot. Now, if you had a "topping off" type of high frequency switching power supply, that could help. Class D/T definitely at this low power, if you want to maximize SPL.
The above comment about 15-30 watts...not normally. It's true if you could feed 3W CONTINUOUS then you could get bigger peaks, BUT BUT BUT you need an unusual amp design like the monster Rockford, which has very large energy storage isolated from the power supply and just topped off by the power supply.
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