bad motor mount wont cause ur car to bog.

When my 02 accord had 20k miles I came across a similiar problem.
I went to take off from the light and the car started to sputter.
As long as I drove slow the car wouldnt bog. Only when I floor it ( indication that more fuel is needed )

I believe and also Honda believed that I had bad gasoline.
The problem never happend again. Honda couldnt even figure out the problem.

So maybe it could be fuel related.

clogged injectors, clogged line,. I would try and use that fuel injector cleaning stuff.