A delighted Charlene Barter had the honour of scoring Bohs' first try of 2014, and an excellent conversion was added by Nicole Fitzgerald from near the touchline.
It took another 20 minutes for the second try when Ireland Grand Slam star Joy Neville, who made a most welcome return to the game, crashed over for a well-taken effort.
Fitzgerald was once again successful with the conversion. Just before half-time Mollie O'Donnell got in for the third try to make it 19-0 at the interval.
The second half started well for the hosts when Valerie Mitchell crossed for the bonus point score. This was followed shortly afterwards by a blistering solo run by Sara-Jane Cody who broke through a number of attempted tackles to score try number five.
Aine Staunton made some powerful runs and also some brilliant kicks deep into the opponents half and got in for the sixth try on 63 minutes.
The final try was scored by strong sprinter Louise Galvin and converted by Aine Staunton, with the player-of-the-match honours going to Slavica Radic.
Fellow Division 1 side Blackrock lead the way in Pool A following a 41-7 victory away to Enniskillen, while St. Mary's got a walkover in the first round from Belfast Harlequins.
Top flight table toppers Old Belvedere were the biggest winners on the day, emerging as 65-5 victors over a game Navan side at Anglesea Road despite the tough playing conditions and missing their Ireland internationals who were away at camp.
Also in Pool B, Railway Union came away from Cooke with the spoils, winning 27-7. Their successful All-Ireland Cup debut produced four tries including one from player-coach Mere Baker, who played international rugby union and rugby league for her native New Zealand.
The wet weather had the biggest say on the Pool C opener between New Ross and Rathdrum which ended in a 0-0 draw.
The Wicklow side had the better of proceedings overall, but the conditions hampered their efforts to break the deadlock in both halves. Much-improved scrum half Lisa Cahill was singled out as their player of the match.
Portlaoise are the early leaders in Pool D following their narrow 5-0 victory away to Carlow, while Galwegians ran out 33-5 winners at Edenderry in their opening fixture in Pool E - Cill Dara have joined this pool following Buccaneers' withdrawal from the competition.
The winners and runners-up from Pools A and C will advance to the quarter-finals of the Cup as both pools contain five teams.
The winners of Pools B, D, E and F will also advance to the Cup quarter-finals with lesser ranked teams then qualifying for Plate, Shield and Bowl competition quarter-finals.
The final fixtures of the Round Robin phase are scheduled to be completed by Sunday, February 16.
The Cup quarter-finals will take place on Sunday, February 23, semi-finals on Sunday, March 2 and the finals will take place on Sunday, March 16.
2013/14 WOMEN'S ALL-IRELAND CUP:
FIRST ROUND RESULTS - Sunday, January 12
Pool A: Enniskillen 7 Blackrock 41; St. Mary's received a walkover from Belfast Harlequins
Pool B: Old Belvedere 65 Navan 5; Cooke 7 Railway Union 27
Pool C: New Ross 0 Rathdrum 0; Carlow 0 Portlaoise 5
Pool D: Edenderry 5 Galwegians 33
Pool E: UL Bohemians 41 Shannon 0; Nenagh received a walkover from Young Munster
Pool F: Highfield v Ballincollig was postponed; Tralee v Fermoy was postponed (Pitches unplayable)