We have the XBee Bluetooth module set up on a separate breadboard. We are then connecting the send and receive of the Bluetooth module to the tx and rx (pins 0 and 1) pins of the arduino. When we try to upload even a simple program to the arduino, such as blink, WITH the wires attached to the Bluetooth module, we receive an error message that says "out of sync." even when we do not receive this message, the program does not run correctly, such as the blink program will not blink. When the wires are removed, the sketch compiles and uploads successfully, but reinserting the wires after the fact does not help with what our code is trying to do (hold the LED high for five seconds and then blink if the Xbee is connected). We have tried solving this by resetting after the sketch has been uploaded, but it hasn't fixed the problem. Please help!
Your question is not clear. Please show a schematic or a photo of your setup. Usually people around here jump to help you if you provide details and ask clear questions :)
If you're saying that the module is connected to the Arduino TX and RX pins while trying to upload a sketch to the Arduino through those same TX and RX pins (via the USB-to-serial adapter), then it's no wonder it doesn't work. You have three devices (USB-to-serial, Arduino, and the XBee module) on a private serial link meant for two. :-)
Unless I misunderstood, and you're uploading the sketch VIA Bluetooth instead..?