If you're in Needham Market, you might think about joining Suffolk Riders.
Regular Sunday rides, usually leaving from Martlesham. Sometimes half day, sometimes full day.
Monthly fish and chip runs on a weekday evening, leaving from all over
Monthly club nights in Needham
Other random rides
Two or three tours a year, usually abroad
They're a good group of people - although it's true that old blokes feature more prominently than in the general population - some very good riders among them, though. It's a RoSPA group, so they'll invite you to do the advanced training marlarkey which you might find worthwhile if you haven't already done it. They offer a lot of different kinds of rides, so chances are there's one there that it like what you're after. For all I know you're already a member
If it's a more casual thing you're after then, if you're on FB (which is how the biking world meets up these days) check these out
Suffolk Biker Family
FTWUK - it has a strong Suffolk bias
OTT East Coast Ride Outs
Then these aren't ride outs, but I guess you know about the bike nights at Stonham Barns? Also Krazy Horse in Bury hold a few bikes nights in the summer - they're always popular. If you're up for a slightly longer ride, Two Wheel Tuesday, held all summer on Tuesday (who'd have thought it...) evenings at Old Buckenham; it's always rammed when the weather's good, has a nice vibe.