They not only threw the ball around - at times they threw caution to the wind. Had it not been for the prowess of their pack things might have turned out a lot differently.
Gareth Delve, one of the shining lights in the Bath eight, admitted: "That was one of the quickest games I've played in this season. It was hard work and the return match is going to be a real battle."
Delve, a Welshman, was one of the players contributing to the pace of the game. Time and again he would power over the gain line before making high-quality ball available. He was flawless in defence, read the game well and supported team-mates. It can only be a matter of time before the Wales coach, Mike Ruddock, sends for him.
The England hooker Lee Mears also made a big impression. He made one superb break, selling the opposition a dummy on the way, and when he retires from rugby he should take up darts, because he is one of a rare breed - a hooker who can throw in accurately.
He too found the going tough. "That was a full-on match," he said. "We were disappointed to have conceded so many points. But we did score four tries, and at home."
That was certainly a feat, given that Bath have not scored a try at the Recreation Ground in the Premiership all season. But as it was they did not pull clear of a tenacious Glasgow side until a scant 10 minutes remained, when the tank known as Salesi Finau rumbled over on the right wing after some slick handling.
The Scots were magnificent. They had arrived with no points and no hope but they left with armfuls of respect and, more importantly, self-belief.
Although Brian Ashton is not due to take over as director of rugby until the new year, he is apparently going to accompany Bath to Scotland for that vital return match. He and his players are clearly aware that much needs to be done over the next four days if they are to come through successfully at Firhill on Friday night.
Glasgow's coach, Hugh Campbell, said: "Firhill suits our style of play. When we played Edinburgh there in a Celtic League match last week we beat them comfortably."
If Bath cannot fit their new, free-spirited approach to the discipline of their pack, they could well go the same way.
Bath: Tries Welsh, Stephenson, Lipman, Finau; Conversion Barkley; Penalties Barkley 3. Glasgow: Tries Henderson, Parks; Conversions Parks 2; Penalties Parks 3, Gregor.
Bath: M Perry (M Stephenson, 16); S Finau, T Cheeseman (A Higgins, 76), O Barkley, F Welsh; C Malone, N Walshe (A Williams, 76); M Stevens, L Mears, D Bell (D Barnes, 59), S Borthwick (capt), P Short (R Fidler, 66), A Beattie, M Lipman, G Delve.
Glasgow: G Staniforth; H O'Hare, G Morrison, A Henderson, R Lamont; D Parks (C Gregor, 72), G Beveridge (capt; S Pinder, 48); K Tkachuk (L Harrison, 40), S Lawson (F Thomson, 57), E Murray (Tkachuk, 62), T Barker, C Hamilton (D Turner, 57), S Swindall (G Hayter, 63), J Barclay, J Beattie.
Referee: C Berdos (France).