You may have preconceptions of bellringers. Personally, I've never met one. The Central Council of Church Bell Ringers say that "bellringing is a great way of making new friends and meeting people" and that it's "a really different experience" so maybe now's the time to join them. The next big national bell ringing in the UK will be for the 200th anniversary of the Battle of Trafalgar in October, so there's probably enough time to get up to speed.
For a more freestyle approach why not visit St Anne's Shandon in Cork City? Here you can ring all the bells yourself without getting told off. It's a basic hand-operated pulley system rather than the swinging on a rope arrangement, but they thoughtfully provide music for a couple of songs. There's a lot of pleasure to be had from making that much noise. While you're there you should take a day trip to St Colman's Cathedral to hear Ireland's largest carillon.
Listening to BBC Radio 4's Bells on Sunday is a more passive experience. You'll get to enjoy a different set of bells every week, although I'm never up early enough to catch it.
Of course, nowadays it's all done with computers. InspiredCode's ChurchBells software for Windows is a terrifying insight into the world of the campanology enthusiast: a belltower on your desktop.