For anyone interested in converting your bike, I found the exact answer
I was looking for here: http://www.motorizedfoldupbikes.com/

It's a US company who makes simple engine kits to install onto the back
on a bicycle. Quick release, so I'm not sure how secure that would be
in public.

If anyone would care to look at the website and comment about the
different models of engine available (they have five engines named
under the ENGINE KITS menu on the left).  Unfortunately the people who
made the website decided to give a specification for each engine, but
different statistical information for each one, so its harder to
compare some of the models.

Prices are pretty good though, around $300 to $450 - much better than
buying a complete petrol bicycle all in one.

Ever heard of something called a "moped?"

===========================================
You should consider a complete unit with wheel strength, braking and
suspension designed to match the capabilities of the engine.
The pedals are going to wind up primarily as footrests, since you would
be pedalling extra weight.
Best to just look at a small motorcycle and study the Smith System of
Space Cushion driving to keep yourself alive.
Actually, you'll soon discover that a larger motorcyle can be safer
than a smaller one since you have more power and control.
A small Honda isn't much different from a moped and you get brake
lights and turn signals.
For a real road going bike, an old BMW would be my choice.

What you are looking for is called a Moped.  A Velosolex is one such
animal.

I am in Canada and don't have a source, but they do sell motors to put
on regular bicycles.  They then become 'mopeds' and require lights and a
license and helmet to drive them on the street.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's
Canadian Off Road Trips Photos:  Non members can still view!
Jan/06 http://www.imagestation.com/album/pictures.html?id=2115147590
(More Off Road album links at bottom of the view page)

It is possible to attach a small motor that drives directly on the
tire.  To be honest I think that you will find all of the fiddling to
get it attached and running will not be worth the modest power assist
you will get.  If inexpensive transport in heavy traffic is what you
are looking for then consider a moped, or even a small scooter.