Tries from Harry Ellis and Geordan Murphy, plus 16 points from fly-half Andy Goode sealed a 26-14 win at Welford Road and a trip to Twickenham next Saturday to face Gloucester, who overwhelmed Saracens 50-9 at Kingsholm in the other semi-final.
"It wasn't a great performance on the day, but we are through to another grand final," said Howard.
Bristol arrived at Welford Road with the league's best defensive record and Tigers had to work hard for their points, while also showing discipline and determination in defence as the visitors scored just the one try through centre Sam Cox early in the second half and three penalties from fly-half Danny Gray.
"We expected them to be tough up front, they are experienced campaigners and they did really well,"said Howard. "A year ago we won well against London Irish in the semi-final and then did not turn up the next week and lost badly in the final.
"We have been to Twickenham for one final already this season and won. We are in there again and it is now down to a one-off game."
With the EDF Energy Cup already won after victory over the Ospreys last month, and the Heineken Cup Final against London Wasps to follow, the Guinness Premiership showdown completes the set of Twickenham visits for Tigers this season.
"We are very proud of what we have done in getting to three finals," said Howard. "But now we are in one-off finals and have two very hard teams to play. The guys have had a lot of tough games recently, including the Six Nations for some of them, so it has been very intense. The players deserve an immense amount of credit and respect for that."
Howard will have to check on the fitness of scrum-half Harry Ellis and wing Tom Varndell as he prepares for the final two games of the season after both suffered injuries during Saturday's game. Prop Martin Castrogiovanni is still sidelined by a hamstring injury.