Bard is a lot older than both babs and dick so he most likely wasn't in the same friendship circles as them and she for sure wasn't dating him by the end of S2 since that would mean she was cheating on him with Dick so I think it's a lot safer to assume he met Babs in the physical physiotherapy since Bard has a prosthesis leg
Between S2 and S3 theres a 2 years timegap and within these 2 years:
- barbara got paralyzed
- She became oracle
- Started her first serious relationship with Dick at least a few months before S3
See it's just hard to fit a relationship with Bard here, I do think she meet him during this timegap but she was going though a rough time and not really interested in starting a relationship with a stranger
And then theres the 6 months/1 year timegap between S3 and S4 I think it makes a lot more sense to assume it happened between this timegap
- Barbara and Dick break off for some reason
- Barbara is already friends with Bard and accepts going out with him, they date for a few weeks
- Barbara decides to forgive Dick, dumps Bard and get back together with Dick
- Feeling bad for dumping Bard like this she sets him up with Artemis