I would agree with GaryH. Using a 1/8" straight bit. clamp a straight edge on to your board so you can get a straight line. Make sure the bit is locked in very tight (I've had problems with my straight bits creeping down) and make multiple passes until you get teh depth you want. depending on how deep you want the groove, doing the entire depth at once is asking a bit much out of the bit.
Now some may disagree with me on this, but since you are using MDF, I would get the cheapest bit you can find and plan on throwing it away when you are done. Why? My experience has been that MDF dulls a bit/blade like nothing else so why dull a nice carbide bit. I use the same theory on my saw blades with MDF. By a cheap one and throw it away at the end of the project.