I used to breed and show dogs and I like to spay my own pet bitches midway between their first and second season. I've never had any problems when my girls are on heat. The important thing is not to advertise the fact your dog is in season. Don't take her for a walk. She will leave a pee-mail trail telling every dog in the area she is available. If you must walk her then put her in the car and drive to an area away from home.
I always kept my in season girls in the house. They only went outside under supervision. Some bitches (especially Collie breeds) are very clean and leave no blood spots at all. If you have a "bloody" bitch you can buy Bitches Britches or similar for wearing indoors.
Earlier this year my Sheltie Kenna had her first season. Unfortunately it was a week after the arrival of our new 20 month old Whippet Strada, an entire male. I contemplated putting one of them in kennels but then decided to brave it out. Strada had the front yard and the front of the house. Kenna had the back yard and the back of the house. The only real danger time was mid cycle when Kenna was a real tart for 4 or 5 days. Extra vigilance was needed then but overall the whole thing went quite smoothly. No accidents.
Our yard is fenced for Deerhounds so the fences are very high and non climbable. Even so I would never leave a bitch in season outside unsupervised. Without the complication of the male Whippet, Kenna's season would have been a breeze to cope with. Extra play time made up for no walks.
This is not meant to be critical of other people's experiences. It's simply a system that has worked well for me on many occasions. Hopefully it may be of help to others in the future.