It seems like some of your senior colleagues may be quite insecure. It is a classic scenario that someone younger joins a team with new ideas, more recent education and training, and this makes some older team members insecure about their own abilities. Instead of welcoming new people with skills that will strengthen the team, insecure people think only how it will affect them personally - how it reflects on them if you can do something they can't, and possibly how you might go on to bypass them.
I would say you need to be balanced in your attitude and approach to this. On one hand, try and see it from your colleagues' point of view. You don't necessarily know what promises your colleagues may have been given about their own careers that didn't happen. They may have been promised training and development, or career progression, and if that hasn't happened yet then they might be angry about that and (unfairly) projecting that onto you because you're the new guy with a fresh outlook. On the other hand though, it is unreasonable of them to demand you bug fix something they can't, especially when the code was somebody else's and the bug arose when they were giving it to you.
Don't respond with rudeness if someone is rude to you at work. If you set out with the aim of firing an insult back or proving them wrong in a very public way then you might end up looking bad yourself. Remember you are still new and while you might know a few extra workarounds than them there is no substitute for experience.
Use the project you are working on to prove yourself. Research the problem and fix the bug if you can. If not, try to implement the workaround in an automated way so it is as good as a fix. Alternatively, can you see a way that the bug could be avoided if you built this code again from the ground up?
I found myself in a similar situation a year ago, and after a year it has almost completely resolved itself. Ways I have found work to improve the situation are:
Even if someone has irritated you, show them respect as a senior and ask them for advice on some things. If they have an ego problem this will puff them up a bit and feel better about themselves and their skill-set. If they feel less insecure they may treat you better.
Focus on your own work and quit suggesting ways they could do theirs better. The longer they spend struggling with bugs of their own creation the less time they have to interfere with your work.
If the rudeness persists from specific individuals you may consider going to your manager (or their manager) about it. But don't do that too soon - get a few successful projects or pieces of work under your belt first. That way your manager will see it as a concern raised by a valued member of staff rather than "the new guy causing trouble".
One year on in my role and I have my own workload which built up over time, and this keeps me separate from anyone that was a little rude when I was learning from them / job shadowing in the beginning. I have built up working relationships with more people and know where I stand with them, so I know they wouldn't listen to one or two people who might be rude. And the rude people have softened. If they are still a little sarcastic towards me on occasion I feel comfortable either ignoring it, or else I have the knowledge and experience to dismiss it.
