Is it possible to get or build a solar charger that will trickle charge my Sealed Lead Acid (SLA) battery pack while riding to extend its range? The pack consists of three (3) batteries of 12V, 12AH wired in a series.

I don't know. Sounds dangerous. You are saying charging and discharging the same battery at the SAME time? I don't like the sound of it. You would best have two packs. One for use, the other for charging and hook up some switch to it. I write this for your safety friend.

Got a trailer for that bike?

I wonder if it is possible to add the solar generated current directly into the motor? If if your motor was providing 100 watts, maybe solar power can add another 20 watts (not sure how large of a panel that would require).

Here is another way to phrase the question:

Can I take this folding solar panel which outputs 6.5W:
http://i32.tinypic.com/6zas5z.jpg
http://www.canadiantire.ca/browse/product_detail.jsp?PRODUCT%3C%3Eprd_id=845524443281438&FOLDER%3C%3Efolder_id=1408474396672503&bmUID=1215034936542&deptid=1408474396672395&ctgrid=1408474396672406&subctgrid=1408474396672503

along with AC charger which came with my electric kit,

and when stopping for breaks and meals during a long ride, use the combination to trickle charge the Sealed Lead Acid batteries? This would extend my bike's range and prevent over-discharging the SLAs.

Note, when I return home, I always plug the SLAs back into the wall plug after*EVERY* use. No exceptions.

Would this work?

Cars already charge the battery while discharging it via the alternator and lights, stereo, etc. There is nothing at all wrong doing so. The problem will be getting enough square footage of solar panel to do the job. I am contemplating a solar battery charger for a 24v 10ah battery and I am going to need a 63 watt solar panel to get that done in 5 or so hours (the number of sun hours for your location). A 65 watt panel is this big:
Mechanical Characteristics
Dimensions (LxWxD): 43.7" x 19.8" x 1.97"
Weight: 15.9 lbs (7.23 kg)
Frame: Clear anodized aluminum alloy type universal frame; Color-Silver; Standard junction box


A 15 watt panel in the sun for 5 hours will provide 75 watt hours (less losses) a 36 volt 7ah battery has 252 watt hours in it. So the 15 watt panel could extend the range up to 30%. A 15 watt panel has these specs:
dimensions: 12.40'' x 36.42'' x 0.75"

Mounting that may be difficult, but not impossible. You will also have to get a 36v panel, not a 12 volt panel.