I'm no irrigation guy, but I'll still throw in my 2 cents.
When we've needed to go under sidewalks for low voltage landscape lighting, we have found the easiest thing to do is pound a pipe through. Granted, a 4' wide sidewalk is a little bit smaller than a 20' driveway, but the concept should still be the same....
Here's how I would attempt to do it, short of spending the money on one of those Borezit tools:
Dig a trench that is slightly deeper than the driveway concrete. Trench needs to be about 15' long.
Get metal conduit (or normal pipe), big enough to slip the PVC into. The conduit will be a sleeve, as was suggested in an earlier post. I think conduit comes in 10' sections....
Thread the ends of the conduit and add a short section to the end of one piece. The short section will be the "beating section".
Here's what I would do differently than anyone else. Flatten the end of the conduit that is the leading end. Don't cap it. Put the end of it on the driveway, and flatten one side, turn over and flatten the other side. The end needs to be completely closed, lest you end up with a pipe full of gravel and dirt (trust me, I found this out the hard way the first time I did this).
Start pounding the pipe through. When you get to within a foot or so of the first section being completely under the drive, take off the "beater" section, and add on the second section. Continue until the pipe comes out the other side of the driveway.
Cut off the beating end, as well as the flattened end, and put the PVC through.
I timed myself on the last sidewalk I did like this, and from start to finish (begining to dig the trench until the flattened end was cut off), took 15 minutes. That was a 4' walk and 3/4" conduit, so I would have to guess that a 20' drive would probably take me around an hour or so with a slightly bigger pipe.
HTH. Let us know what you end up doing.
Dan