I am not familiar with the Bounder or with Direct TV - we have Challenger and Dish. First off our coach has a HDMI running to each TV throughout the coach from a single HDMI control box and along with a standard cable connection. Our control box allows for connection from 2 sources. In our case it is a connection from our Dish receiver and a DVD player. This is important as you distribute the signal to each TV.
Our Dish TV has a VIP211z receiver. The VIP211z has a HDMI out, a composite out and an in from Dish Antenna (in our case a Tailgater). This is important because there is not a direct way to output from the receiver to the TVs through standard cable connections.
In our case, you simply plug the antenna into the cable in connection for the coach. Again in our coach, I added a splitter for the cable connection to provide a connection for the VIP211z and to continue the input to the TVs via the standard cable connection. Make sure you use satellite splitter. The VIP211z sends a small electrical current back down the connection to the Tailgater to provide power. The satellite splitter isolates this current to the Tailgater only otherwise it will make the cable signal "fuzzy".
From the back of the now connected VIP211z a HDMI cable is run to our HDMI control box.
With this configuration your are done. You will have signal via HDMI to each of the TVs.
IF and only IF you do not have HDMI running to each TV in your coach you will need to run signal back to a RF Modulator. I explained the connection for the RF Modulator in this post. It is at this post: Tailgater on Challenger 37TB
It really is simpler than it sounds.