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The 28-year-old joins the National League South club with more than 100 appearances for Cambridge United, and has also played for Eastbourne Borough during the latter stages of the 2025/26 season before moving to Chelmsford City for the current campaign.
May joined Swindon on loan from Portsmouth for the 2019/20 title-winning season. Then-manager Richie Wellens had previously tried to sign him permanently.
The midfielder did not secure a regular place in the team, largely due to the presence of Anthony Grant, Michael Doughty, Jordan Lyden, and Danny Rose ahead of him in the pecking order.
In all, he made 13 appearances for Swindon, although only one of those was a league start, and he returned to Fratton Park from his loan during January.
May joins up with fellow former Swindon players Harrison Minturn and Harry Parsons at Twerton Park. The 28-year-old may remember sharing the pitch with Parsons during an EFL Trophy match against Bristol Rovers.
The trio are part of a Bath side in fine form in the Southern League Premier South, as they presently sit in the playoff positions, but they are only four points off the top spot and have won all of their last four matches.