How to perform a long-distance bunny-hop? When I need to clear a missing pothole or a slippery section of the trail, I try to make the hop as long-distance as possible. The result is that, unlike when hopping onto something elevated, now I push the bike forward while in the air in order to "place" it as far as possible forward. The drawback is that I am getting closer to falling off the back of the bike.

Is this smart? What other techniques exist for jumping the furthest at fixed approach speed?
Some points.  


If you bunny hop by getting both wheels to leave the ground at the same, the rear wheel has to jump the length of the obstacle plus the length of the bike to clear the obstacle.
A more modern, trialsy and BMX-y bunny hop is what is what is sometimes called an 'American bunnyhop'.  In this, the front is hauled up first, then the back as the front is being pushed down (tutorials are available on youtube, other video sharing sites are available).  This means the back wheel can leave the ground later, and so doesn't have to jump as far as in the point above.
Your time in the air is determined by your height, your distance traveled in that time is determined by your speed.  So jump higher while riding faster and you'll go further.  (And, potentially, crash harder.  Every silver lining has a cloud.)
When mountain biking, simply "unweighting" can often be enough to help an already rugged and quite probably suspended bike better cope with rough patches.  And if all else fails - just get the damn front up and over!