This is a question that most priests get asked on a somewhat regular basis. The answer is not a simple one, so I hope you'll allow me a few paragraphs to respond.
1) Everyone knows that the answer to the question is supposed to be "absolutely not!" but it is undeniable that some priests DO want to be bishop, and quite badly. It isn't widespread or anything, but it is there.
The question arises here - why would a person want to be bishop?
The reason, it seems, is that all Catholics ask ourselves a question - "will I go to Heaven?" - and, as a young Catholic author recently noted, only half jokingly, we also ask ourselves another question somewhat regularly: "am I the anti-Christ?"
Getting named a bishop, by the Pope, certainly has some appeal because it could be seen as the Church (and thus Christ) saying - "This guy is holy and a winner and saintly, that's why we made him a bishop"... I understand the appeal of that selection, even though I also know it doesn't work that way.
St. John Chrysostom once said “I do not think there are many among Bishops that will be saved, but many more that perish.” The Saint also noted that "The road to hell is paved with the bones of priests, with the skulls of bishops as lamp posts along the way."
So while it makes sense, on a human level, to desire to have some external authority like the Church select you for something, being selected to be a bishop doesn't ACTUALLY have any bearing on one's eternal destination.
2) The people that get selected to be bishops are men who hopefully display holiness and the traits of Christ, but of course practically a bishop also needs to be a leader. Bishops today oversee tens of thousands of employees, manage countless priests and lay leaders, and are, practically speaking, the CEO's of some of the biggest civil corporations in their territories. So getting picked to be a bishop has a lot of practical considerations involved as well. You hope to find a guy who is holy AND a good leader, but no one can truly judge holiness except God. I think the Church looks for men with practical leadership skills and does the best any of us can at judging a man's character as well.
3) The job of a bishop is huge, intimidating, and scary.
When I imagined my life as a priest when I was discerning priesthood, I imagined doing what I'm doing now - a couple of smaller parishes, youth events, Masses, baptisms, funerals, stations of the cross, soup dinners, visiting nursing homes, etc. A bishop has almost none of that. It is meeting, after meeting, after meeting, after meeting. And then there's the weight of the responsibility - surely it would be crushing if not for God's Grace - and it all just seems overwhelming. I just wouldn't want that.
I look at the two Archbishop's I served for, and I don't envy their life. What they do is actually a great sacrifice of a lot of meetings and management at the loss of all the one on one interaction and ministry that parish priests have.
I don't even want to be the pastor of some mega-parish, so I can hardly fathom the emails, meetings, photo ops, and all of the other things that a bishop has to deal with.
So when you add all of this up, I am very happy being a parish priest. I hope that helps provide some insight into what a bishop's life is like, and why anyone who chases it for any other reason than to lay down one's life for others just has not truly grasped what they are chasing...
But then again some men, as Jesus noted, will always "love places of honor at banquets, seats of honor in synagogues, greetings in marketplaces, and the salutation ‘Rabbi.’" (Matthew 23:6)
Keep your bishop in prayer because it is a tough gig. That's why we pray for him, by name, at every Mass