I don't have a car and I manage quite a few Audaxes.
Living in London makes it easier as there are usually direct trains to most destinations (all of the main London stations are within a 10 mile ride from my house, and under 3 miles from work). I think this is the main reason why it's much easier for me compared to the other stories above...
For local-ish rides I'll cycle anything up to 50km to get there:
* 40km to the start of the Willy Warmer one year.
* 75km to the start of a 100km Audax so I made it into an ECE 200 (well, DIY+Cal back then)
Only on a couple of occasions have I blagged a lift in a car (through posting on here) but that just made it easier, I could have still got to the start by riding or getting a train.
Just be prepared for early starts. Riding The Upper Thames meant getting the 5.21am train from Putney to Reading. I was up just as early to get to the Taste Of The Test 200. Using a car would have given me two hours extra sleep.
For events further away (and where the trains don't run early enough in the morning), often longer events, I'll travel up on the Friday night after work by train and stay somewhere nearby.
For the Bryan Chapman I got a train from Paddington at 6.30pm to Bristol Parkway. There by 8pm and then it's a 10 mile ride over to Severn View Services and the Travelodge. Travelodge booked for Sunday night again and an early train Monday back to London and straight in to work. Work don't mind me being late the occasional day, so even getting in at 10.30am isn't a problem, I could do it by 9am but I value the extra lie-in.
The Dean is another train on Friday night and 2 nights at the Peartree Travelodge (I've never finished in time to get a train back to London). If it's a nice day on the Sunday I'll cycle the 100km home from Oxford.
For the Midlander Super Grimpeur it was an evening train (6.30pm or 7pm) from Euston to Birmingham, local train to Moor Green, and then a nearby travelodge (booked for 2 nights). Finish the ride, back to the hotel for more sleep, up and get the train(s) home.
The recent Snowdon and Coast was a slow (but direct) train from Marylebone to Shrewsbury. Got in to the Travelodge at 10.30pm. Up at 6am to get to the start. Ride the event and back to the station to get a train home (it helps being slow).
This does sometimes limit my choice of Audaxes. I'd rather not have to stay away on the Friday night, but I haven't found a ride I couldn't do if I really want to do it.
Good deals on Travelodge prices and train tickets if you book long enough in advance and are prepared to be a little bit flexible. Most of the time I pay under £30 a night for the hotel room and under £20 for a single train ticket.