What are the correct wiring connection when the supply has 4 wires for installing a ceiling fan with light set and remote control? Red, Black, White, and Bare. The Bare is ground, the white and black is power, but my concern is the red. My assumption is the red wire goes to the light kit set.

Many I see have a black and white in, and then white for light and fan. Also 2 wires(1 for light, and 1 for fan.
Black is usually Fan, and Blue, Red, or Black/white is to light.
Do you have 2 whites from remote unit?

I have two wires coming out of the remote control transmitter for the supply connection. The wires are Black and White. The remote transmitter has Blue, Black, White and Green coming out on the other side for the ceiling fan and light set connections. My house supply wires are Red, Black, White, and Bare. I connected the House supply Red to remote transmitter Black, house supply White to transmitter White, house supply Bare to Green wires from canopy Green, Transmitter green and Fan Green, and I left the house supply Black wire end covered. I connected the other wires from the transmitter to the ceiling fan/light set to the exact colors Black to Black, Blue to Blue, and White to White. I can now only control both fan and light set with the same light switch. Previously I had one switch for the fan and another one for the light set. My fan switch is now disabled. Can I connect the Black wire to control my fan with the other switch? If so, what is the proper configuration to do so? Or with this configuration I can not use both switches?

If it is the unit I think you have. Light/Fan to be controlled by remote, not switch. Don't Quote me.
Don't think you can Use 2 switches, unless you connected red to blue?(Ceiling Light wire to fan Light wire), Bypassing the receiver. Light would be by switch, and fan by remote.
I would check fine print in instructions, Particularly 2 switches?
Model#?

You are absolutely right. With this remote configuartion you can control the light and fan with one switch. You cannot use the 2 wall switches to control the fan and light if you are using the remote control. You must connect the red supply wire to the black wire on the remote transmitter side and the white supply wire to the white wire on the remote transmitter. The wires coming out of the remote for the fan & light set connection should match its colors. I connected it right the right time, but I wanted to attempt to control the fan & light set with its separate wall switches, but that will not work. Thanks :)

The above is correct.

You can only use one hot wire and switch, and have to cap off the other, with a remote fan.

Ceiling fan wiring - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-wiring.php)

How remote control works for ceiling fan ?

What make and model fan do you have? Many are different.