Depending on how rocky & tight your soil is, but it's possible to dig a ~12-13' long 12" deep trench on one side, and use 10' sections 1" steel pipe with a caps on both ends and drive it through with a 25lb maul, spinning off the cap you're driving, adding a coupling and another 10', capping it, repeat unit you're sure you've driven enough pipe that you're sure you're here, then go dig it up on the other side.
I've done exactly this a couple of times in sandy soil at about 20', no reason it couldn't have gone 30. A 10' section of 1" pipe is pretty snaky stuff when you put the hammer to it- you have to line it up well, and know that it could change direction on you as it engages obstacles. One big rock could spoil that approach if it dead-ends, but smaller rocks, not so much. It'll never come up exactly where you think- always deflects a bit- it could end up either shallower or deeper at the far end. But in consistent and not-too-hard soil it's not that bad.
I got the idea from seeing a 40-50' county road crossing for 2" PVC water main being installed this way. They were using 3" or 3.5" galvanized steel pipe and a backhoe to push it through. The push-pipe was abandoned in the end, used as a protective casing for the 2" PVC threaded through it, saving the contractor a lot on time, labor and road-repair costs etc. It was pretty slick- mostly clay subsoil in that case, and it took them less than an hour to make the crossing. The water main contractor had an electronic pipe-finder gadget to figure out where to dig on the far side, but in the shallower shorter driveway crossings I've never had a problem finding the pipe. YMMV.