Amp to powered subwoofer question

I'm using these Dared VP-20 quazi mono block amp I have just acquired.
I'm using them as integrateds. I'm running them to bookshelfs and a sub.
These amps don't have a rca line out to hook up to the sub that way, so I'm taking wires and running the sub fron the ONE of the mono amps speaker leads.

Heres the thing I'm concerned about,my sub like to have two input to get a full sound out of it, so I jump the other side of the terminals on the sub, kind of like you would with a speaker you can bi-amp.

Is this causing a problem for my mono block amp?

It seems to work fine...
Run the left mono block speaker out to the subwoofer left speaker in. Run the right mono block speaker out to the subwoofer right speaker in. Connect your left bookshelf speaker to the left subwoofer out and the right bookshelf speaker to the right subwoofer out.
Thanks for the comment.
My room is not set up to run the wires that way.

I prefer to run one line to the sub,it goes from one of the mono blocks, into the floor, through the basement, up through the floor to the sub.
So,one line is my preference.

I just don't want to strain the amp and I'm wondering if I bridge the conection, on the inputs on the sub, if that's cool or not.

Plus, I want to run my Bookself speakers full range,with their own speaker lines coming off the amps.

You have to run both channels to the sub. Period.
Either use Y cables to run both pre-amp outputs to the amps and sub or run both sets of speaker leads to the sub, then the speakers.