People taking bitches in season, particularly during the fertile period, out walking make me really cross. The scent given off by an in season bitch can cause an enormous change in the temperament and behaviour of male dogs, which can take months for the dog owner to put right.
I only have bitches, but would never walk them where other dogs are during a season.
A season lasts for approx 4 weeks or 28 days and the fertile period can be at any point from day 6 to day 22. More usually, the fertile period is somewhere between days 10 - 16. Sometimes the bleeding turns straw coloured, sometimes it stops, sometimes it starts again after the fertile period and sometimes it doesn't.
Don't underestimate the enormous change of behaviour your bitch will display when she is fertile. It is usual for them to stop at nothing to try to be mated - and the same goes for a dog. A tie can occur in the matter of seconds.
If you do decide to walk her and the worst happens, don't panic or shriek, or take it out on the male dog. Get down by the bitch and cup her vulva with your hand to prevent the males penis from penetrating while you wait for the dogs owner to arrive.
To be honest the half hour you would have spent in the park could be equally well be spent training in the garden for the few days a season lasts.