Irishboy, born and raised right here in Bhaile Átha Cliath. Fly out of EIWT.
Flights from DUB to LHR are a f$@king rip-off. The cheapest flight is IR£354 with BMI. That's business class. An economy class ticket would have cost IR£405!!! Crazy or what? I had to ask if she was having me on. Aer Lingus is about the same price, but with all their industrial relation problems at the mo, I'd be worried that the one day I was due to travel they would be on strike! Bloody unions!! You could go to one of the other London airports for less, but you'd have a bit of a trek to Cranebank.
As far as I know, if you are a student or you are unemployed, BA will pay for 100% of your travel expenses. If you are working, they will pay 75%. So, you may as well enjoy travelling business class.
That only leaves the cost of accommodation to burn a hole in your pocket. You can get some decent B&B's around the Hounslow area for £40-£50. If you go for this option, try to get something near the tube. Hotels around the Heathrow area cost from GB£65. I stayed in a B&B in Hounslow last time I was over. I think I got about 3 hours sleep max. After recommendations from fellow PPRUNER's I've opted for the Heathrow Travel Lodge this time, GB£69. It may be more expensive than a B&B but if I can get a decent night's sleep and a good breakfast the next morning, hopefully I can do a little better this time.
Best of luck...