I took my cpap on RAGBRAI. My CPAP (a Respironics) has a 12 volt input so it is a relatively simple thing to hack together a long cable for a cigarette lighter. All of the stuff is available at Radio Shack.
This is much more efficient than an inverter. If you only use the CPAP and no heat or humidity, the draw will probably be less than .5 amps. A car battery can handle that no problem for 8 hours. I've done it many times. The alternative is a deep cycle battery that you charge in a car during the day and then put just outside your tent.
2007 TerraTrike Cruiser (XL) Trike
2004 Rans Stratus XL LWB Recumbent
1999 Trek Navigator 200 21"