Does Bi-amping double the power?

Bi-wiring does nothing significant to the power output. Usually those terminals are wired in parallel. Great if you have speakers in two different rooms, but they do not have "more" amplifier. They are just convenience terminals.

The driving electronics and limits are the same.

Depending on what you are using, you could actually be cutting your power.  What Happens when you hook A Speakers + B speakers both up is that your Amplifier (I assume Receiver) either parallels or series the connection. So if you are using a SET of 8 ohm speakers on A, then add a set of 8 ohm speakers on B, your amp if Paralleled will see an 4 ohm load, but if it Series the connection, your amp will see a 16 ohm load.  In my experience only older lower price receivers have done series wiring, but if it did, your 35 watt per channel will be less.  Anything today with a decent power supply should parallel the connection. Bi-amping is done 2 ways.... 
1. 1 amp runs mono playing left channel, 1 amp runs mono playing right channel... 
2. One amp is crossed electronically and runs tweeters and another amp is crossed to only run the woofers.  
I hope this helps, Tim

Thanks @cleeds 

I suppose I meant bi-wiring?

What you're describing will not increase the power delivered to your loudspeakers and is not "biamping." If you want to biamp a pair of speakers, you'll need two stereo (two-channel) amps, or four mono amps, or two mono amps and one stereo amp.

TO DOUBLE THE WATTS YOU NEED AN AMP THAT WILL SWITCH TO MONO EX. MCINTOSH 7270  HOOK UP BOTH AMPS AND GO FROM 270 TO 540 WATTS.