The 23-year-old gained his first group 1 victory on the Graham Richardson and Gavin Parker-trained mare while on a summer riding stint in New Zealand.
''This means the world to me,'' said Bayliss.
''Limited opportunities have stopped me getting success like this, but I've been working hard since I came to New Zealand.
''I'm now a group 1-winning jockey, but I just can't explain the feeling.''
While scoring his first group 1 victory was just sinking in for Bayliss, away from the winner's circle there was concern over the Ellerslie track.
Replays showed Fully Funded, ridden by Sam Spratt, slipped during the race.
After a deliberation, stewards were forced to abandon the meeting with only one race left to run.
''After viewing the film, it was clear Fully Funded slipped twice,'' stipendiary steward John Oatham said.
''We couldn't continue with any certainty for the safety of the riders.''
The Ellerslie track started on at good3 rating before heavy rain caused the racing surface to deteriorate to a slow8 for the running of the Railway.
For co-trainer Graham Richardson, it was a case of 21 years between wins in the Railway.
''I won it 21 years ago and I have had a couple of seconds, so this means the world to me,'' he said.
''We're going to celebrate today and then bring on the Telegraph.''
The trainer produced Kailey to win the race in 1997.
After Volpe Veloce's emphatic victory, Richardson is considering an Australian campaign for her.
''We might even go to the Newmarket in Australia, as Jake seems to think she is up to it, so after a run like that, on ground she doesn't handle, who knows?''
Yesterday's Rich Hill Mile winner, Coldplay, could also be on her way to Australia later this season.
The Murray Baker and Andrew Forsman-trained 5yr-old surprised her trainers with the way she handled the rain-affected Ellerslie track to win.
''We weren't really confident at all, but we thought we'd have a throw at the stumps,'' Forsman said.
''The only thing that gave us a little bit of confidence was the wide draw and she could get out in the better part of the track.''
Like Volpe Veloce, Coldplay has a Trentham feature on her programme before an Australian trip is considered.
''The Thorndon Mile has always been on her radar; a group 1 win is what she wants on her CV,'' Forsman said.
''Beyond that, she could go to Sydney in the autumn.''
The Baker-Forsman stable also landed yesterday's group 2 Avondale Cup with Zacada, under rider Danielle Johnson.
The group 2 Royal Stakes was won by the Donna Logan and Chris Gibbs-trained Hello It's Me.
The group 2 Auckland Guineas was won by the Nigel Tiley-trained Demonetization.
