Operating bicycle mobile requires a major focus on practicality.
Back in my younger days, I tried an 80m 1-transistor transmitter
with a 8.5m (9 ft) whip on the back of my bicycle. I don't think
anyone actually heard me, and I didn't have a receiver (since
the only ones I had at the time used tubes). Later I used the
same whip as a 2m J-pole, and it worked much better.
Getting on and off the bike was more complicated, however, as
I couldn't swing my leg over the back (it would be different with
a recumbent), and, even though the antenna was mounted to
my back axle rather than the carrier, I still ran into problems with
overhanging branches, as the edges of the roads where the bike
paths are often don't get pruned by passing trucks as well as
further out into the roadway.
However, even on 2m FM, casual operation isn't always as
convenient while in motion as one might like. The best
arrangement I found was to have a PTT switch that I could
operate with a finger while still holding the handle bars,
along with a boom mic, which needed to be able to pull free
in case I took a tumble. And "engine noise" (due to heavy
breathing into the microphone) could be an issue, particularly
going up hills.
If you are going to operate SSB, you'll either need to stick to
a particular frequency, or wire the up/down mic switches to a
control on the handle bars. There is no way I would have been
able to tune a radio while riding if I had to grab a knob and
turn it carefully.
Back to antennas: a vertical antenna can work well, and the
"hamstick"-style antennas aren't too bad on 20m and higher
bands, but you need a separate one for each band you plan to
operate. (You might manage to use one on the next lower band
with a tuner, but in my experience they make poor multiband
antennas.) A better approach would be to have one with a tapped
coil where you could (stop and) reset the antenna to change
bands. You may need to build something yourself, although
there are some commercial versions.
You may find that some of the commercial mobile antennas don't
tune well when mounted on your bicycle frame because it is
too small of a ground plane. Using a longer adjustable whip
may help, and I've also improvised by attaching an alligator
clip to the top of the antenna and moving it up and down for
fine tuning.
You certainly could use a typical bicycle flag on a fiberglass
rod as the basis of a mobile antenna if you wanted to build
your own, again with some loss of efficiency due to the shorter
length. I'd suggest winding the coil on a larger former than
the rod itself, however, for better performance. For 15m through
10m, converting a CB antenna of suitable size and mounting
is a good starting point.
The ATAS series antennas are shorter and can be tuned remotely
for changing bands, although they aren't cheap, and efficiency
suffers somewhat due to the shorter length. Those are all
trade-offs that you need to make for yourself based on your
operating goals.
If you know you will be riding out in the middle of nowhere,
with no traffic or power lines, you could try towing a kite
behind you to support an antenna, although the potential
safety hazards must be seriously considered.
If you just want to say you've made an HF contact from your
bicycle, that certainly can be done with a local station, where
antenna efficiency and size aren't as critical. But for chatting
while commuting or riding long distances, then a carefully tuned
vertical can work, but likely will work best when you are on a
calling frequency where other stations will show up, rather than
trying to scan the bands. But you'll have to see for yourself
how much attention you are comfortable diverting from paying
attention to riding to plan ham radio.
You may find some useful information on the
HF PACK group, which
includes bicycles and other human-powered transportation.
They have recommended frequencies, which may allow you to
get by without having to tune the radio.