We get the train down from Glasgow every year. We'll no doubt be on the same train as you as we'll be getting the first train on the Wednesday morning. If it's like the last few years it goes from Glasgow to Carlisle, you change at Carlisle then a train to Leeds.
Once you arrive at Leeds train station there'll be loads of folk going to the fest, follow the crowd or ask someone and you can get a shuttle bus, it's about £10 return which you pay once you get there. The queues will be pretty big but they move pretty fast as there's plenty of buses so I would say that's probably your best bet.
I do think there's a taxi rank nearby if that's what you want to do and I'm sure you could get folk to share.