Points to Note:
Must be water proof.
Has to run on its motor power.
Backlit on Night times.
Must be rugged and shockproof.
Cheap!

 

How about this?

 

Has to run on its motor power.

What happens to the clock when the bike motor stops?

 

The "Display" has to go off but the time has to move on as usual (A small CMOS battery is enough)