Bribes were incredibly necessary for winning the HRE post, even for a couple of centuries after the post became a Hapsburg family title. It was just the way that Germany, and indeed the world, worked. To be honest, they aren't called bribes anymore but the world still works that way. Look at things like the bidding for hosting the Olympics or the World Cup - it's a lot to do with a country's capability to host the event yes, but it's also about their ability to be gaudy and ostentatious and unnecessarily willing to spend money on decorations, and also on the expense and novelty/rarity of the goodies handed out to the decision-makers as thank you gifts. In the medieval/renaissance era, though, there were no people around debating the ethical nature of awarding prizes to those who spent most on winning votes, so the contenders could afford be more public and open about it.
Charles' rivals for the Imperial title were Francis II of France and Henry VIII of England. Henry spent a huge amount on bribes which should have been spent on his defensive project in England, and Francis spent even more but Henry was never going to be elected and Francis was an unpopular choice too so Charles never really had his election in question. The three Kings were the only candidates, though an interesting story is that Pope Leo X wanted Elector Frederick III of Saxony to stand for the position as part of the Papal political campaign to deny powerful rulers important positions, the better to secure Papal supremacy in Europe. This was, of course, the same time that Martin Luther was just beginning to be a nuisance, and the Pope's offer to Frederick was that Luther could be brushed aside and forgotten if he would stand for the Elector position - in return, the Pope would use his influence to secure the position. Obviously if this deal went through, Luther would subsequently create such a stir that he would ruin the whole Pope-being-lenient thing, but then Leo was being manipulative in his dealings anyway so you couldn't expect things to go swimmingly, but a Luther with Imperial patronage would have been interesting.
That said, by all accounts Frederick rejected the offer without a moment's thought. He had no interest in the Imperial title, and he was very much on Luther's side - he had just as much intention of cooperating with the Pope as Luther did (which is to say, none).
Something else to consider: Charles was 19 was he was elected Emperor. Frederick, I believe, would have been 16. Would certainly make for an interesting choice...