I would buy the lift. I've got a Suzuki GS550 that I ride occasionally, but most of the time if the weather is nice enough to ride, I'd rather cruise in the Jeep with the top down. I just keep the bike because it makes a nice second vehicle if the Jeep's down, and it is fun to ride when there's no traffic around.
It would take 20000 miles @ $3.25 fuel to save $3000. Then insurance, registration, and the bike would need 2 or 3 rear tires and 1 or 2 front tires in that time. That's a $1000, So it takes a lot of miles on a cheap bike to save $$. But I would never be without several bikes, BTW. It's a good selling point to the wife, but bikes don't save $$.
I wouldn't do the bike. Too many people texting while driving. I got rid of my Ninja (ZX7r) because of that reason & picked up a couple of dirt bikes. It's cool to throw the bike on the back of the jeep with a hitch carrier, drive to a very remote spot, then take some narrow trails that would be impossible with the jeep.
Just my two cents though. Do whatever makes you happy! Myself, I was starting a family & didn't want to put my life in the hands of a 16 year old girl taking selfties while running 70 in a 55 & applying makeup.