Hi there Arkhamfiend,
The red bubble is an indication that the message did not get sent properly. Common causes of this problem are usually Wi-Fi problems (in which case turning off and then back on your wireless access point may fix the problem) or the people you are trying to send a message to have something wrong with their devices.
Try turning your device off then back on again, and if no luck, try turning off your wireless access point (Wi-Fi router). If still no success, try referring to the following article written by Apple: If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support