I wouldn't be surprised if the bridge with a new electric was just a blank.  MIne was.

On the bright side, it is a little easier than with an acoustic violin, since the pickup for an electric is usually flat.  If yours is, you can just lay a piece of sandpaper on a table and hold it down and sand the feet until they are flat on the bottom.  So that part is a little easier than sanding them to fit the arch like one has to with an acoustic bridge.

Other than that, you shape the bridge the same way as for an acoustic, like the instructions Kevin gave the link for.

The only thing I did different was I used a method that uses a #2 pencil instead of making a tool for the job as Kevin shows.  Same basic idea, though.

I would suggest taking it a bit easy when sanding or cutting wood off the bridge.  If it comes out a bit thick or too high, you can just take a little more off later.  But too thin and it can warp and break, too short and it won't work.  That means buying another bridge and starting over. 

But if you take your time and ask questions when you have to, you can do it.  I had to do the same thing with mine the day it came in, and I had never worked on any part of a violin or even taken a close look at one before.  The bridge I did that day, is the one I still use on my electric, and it works fine.  Has worked fine for 6 months so far.

Not sure why you'd be thinking of using a mute, though.  Electrics are already quiet, so long as you don't plug them into something like a guitar amp and crank it up.