Are speedometers allowed on a bike during a triathlon??

Yes.  The only thing I read on this forum was that metronomes for pace were not allowed.

The only time I wasn't able to use a watch or computer was a fun run where you have to guess your finishing time.

At the Boulder Peak they had a sheriff with a radar gun at the bottom of old stage road, so you could see whether you were over the 35mph speed limit

Were they collecting a "velocity surcharge" for pegging their meter?

Yes.

Now that is cool!

On the Keene Descent at IMLP they had a sign that showed your speed as they are trying discourage speeders but I always loved seeing how fast I was going.

Well, not really.  Because they hand out speeding tickets if you're over the speed limit. 

Really?

You can mount loads of stuff on your bike:  speedometer, cadence meter, GPS unit, stock ticker, just about whatever you want, I think.  (There are limits -- no boom boxes or automatic weapons, for example.)

Now, as for the radar gun:  are we talking about handing out tickets during a RACE?  (If it isn't during a race, well, then, fair enough.  Annoying, and likely not the best use of tax dollars, but fair enough.  If we claim that we should be treated like other vehicles are -- and we SHOULD make that claim (in general) -- then we have to live with the logical consequences of that claim.)

Yes, really! I think it was also a race violation that would result in immediate DQ. In past years before that rule was in place I hit 56 mph in that section.

To the OP: Triathlons do not allow speedometers, watches, Garmins, HR monitors, or talking to your competitors.