They tasted victory in their last PRO12 outing with a 22-7 win over Scarlets and backed that up with a 21-10 victory over Montpellier in Europe.
That win has left them with the chance to secure a quarter-final should they beat their hosts on Sunday and Townsend believes they will need to reach their full potential if they are going to leave England victorious.
"The qualification picture will be a lot clearer by kick-off time on Sunday but we knew all along that we would need two wins from our final two games and nothing has changed in that regard," Townsend told the Scotsman.
"Given the way that Bath have been playing in the last few weeks, this will be a tough challenge, so we will probably have to produce our best rugby of the season to beat them.
"We were delighted with the victory and the fact that it was the first time that the club had completed home and away wins over French opposition in Europe's premier competition.
"It was also pleasing to see the character and belief on display from the players to secure victory in the second half, having trailed 10-7 at the break.
"However, there was also a sense of frustration in that we had a number of opportunities in both the first and the second half to win the game by a more decisive manner and to secure a four-try bonus point."
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Guinness PRO12 Warriors News
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