The classy opening batsman was the star of the show with the bat for Northants, hitting 12 fours and one six in a superb 101 from 98 balls as the Steelbacks posted 308 for nine in their 50 overs.
Saif Zaib hit 61 and Tom Taylor 43 before a battling Bedfordshire side were bowled out for 251 in 44.4 overs.
The visitors were in the game for most of their innings thanks to an excellent 73 from former County man James Kettleborough and 53 from skipper George Thurstance.
Left-arm spinner Simon Kerrigan bowled superbly to take three for 19 from eight overs, while Freddie Heldreich finished with four for 53 from seven overs.
The match was an excellent run out ahead of Sunday's One Day Cup opener against Glamorgan, and Gay said: "When a new competition is round the corner it is nice to get some time out in the middle.
"It is a different tempo to 20-over cricket, it is closer to the four-day stuff, and it is all about timing your innings.
"I think that was what the exercise was about on Tuesday, getting used to that tempo, timing your innings, and picking when to go and when not to go, and I think overall it was a great day for us."
The game had an extra edge for Gay as he hails from Bedford, went to Bedford School, and has played alongside many of the team in the past.
"I am from Bedfordshire and I know a lot of the lads, so there was a bit of that there," he admitted.
"I wanted to score runs against Mr Brett (Tom Brett), my old teacher and old team-mates and stuff, so that was good fun.
"There was a bit of competition out there, but it was also nice to see some familiar faces and get a score."
The likes of Ricardo Vasconcelos, who will skipper the Steelbacks in the One Day Cup, Rob Keogh, Wayne Parnell, Luke Procter, Ben Sanderson and Nathan Buck all sat out Tuesday's friendly, but will come into the reckoning for the weekend.
Gay's century will surely have seen him done enough to get the nod for one of he batting slots for the clash against Glamorgan, although the 21-year-old isn't counting any chickens on that front.
"Tuesday's innings hasn't harmed my chances in any way, but I can't say and don't know if I will be playing on Sunday," he said
"Hopefully I will start, because I want to take my opportunities and play as many games as possible."