They now have to wait for the outcome of Newcastle's final match away to Saracens on Thursday before they discover their fate.
And if the beaten Tetley's Bitter Cup finalists Newcastle beat Saracens by a margin of 30 points, then Bath will still miss out despite this 12- try spectacle in which Jeremy Guscott was outstanding, scoring four tries and setting up a fistful of the remainder.
The London Scottish cause was not helped by the unprecedented loss of their lock Mick Watson, sent off for aiming a butt at Martin Haag after just 42 seconds of what was almost certainly the Exiles' final match as professionals before they merge with Richmond (or whoever) and lose their Premiership place and identity.
Bath had threatened to cut the flimsy fabric of the London Scottish defence to ribbons long before they broke loose, but over-elaboration and over- confidence cost them certain scores on at least three occasions. But in this form and mood, Bath would have destroyed a full complement.
Not that Bath could afford to relax because the Exiles were especially dangerous on the counter-attack. Iain McAusland's pace from deep and his lines of running frequently exposed Bath to the possibility of having to do even more work in order to attain and then sustain that all-important 36-point winning margin.
But it did take a long time for it to sink into Bath's consciousness that Jannie de Beer is a fearsome kicker, whatever the angle or the range.
Midway through the second half, following a marvellous try when Dave Hilton rumbled over after chasing and catching a Mike Catt cross-kick into the in-goal area, and after a raft of Scottish replacements joined the fray, the Exiles had the temerity to turn their courageous counter- attacks into points. Their captain Simon Holmes chipped, ran and scooped a loose ball when Iain Balshaw was caught on his line, but that was all they had to offer.
It meant Bath had fallen eight points shy of their minimum target of 36 points and it was just the spur they required. Guscott grabbed proceedings by the scruff of the neck and put on a virtuoso display.
He sent in Matt Perry and Balshaw for tries while in between there was a moment of brilliance from Catt. He chipped McAusland, gathered on the full and scorched across the line under the posts. Appropriately, the masterful Guscott signed off the season in style with two more stunning efforts and that was that.
Other than a touching moment after the final whistle when all the Bath players made a point of shaking the hand of every London Scottish player.
Bath: M Perry; I Balshaw, K Maggs, J Guscott (capt), A Adebayo (P de Ganville, 65); M Catt, G Cooper (A Nicol, 65); D Hilton (K Yates, 56), M Regan (A Long, 56), V Ubogu, M Haag, S Borthwick, R Earnshaw, B Sturnham, N Thomas.
London Scottish: I McAusland; K Milligan, J Bonney, R Eriksson, J Philip (R Davies, 27); J de Beer, C Mulraine (D Millard, h-t); P Johnstone (C Johnston, 34), D Cummins (D Rudham, 61), P Burnell, E Jones (G Manson- Bishop, 61), M Watson, S Fenn, R Hunter, S Holmes (capt; T Davies, 61).
Referee: E Morrison (Bristol).