I understand that you would like to know when a dog is fertile after her blood tinged discharge starts.
I'm not sure if you are asking the question as a way to determine the best time to breed her to get her pregnant, or as a way to avoid pregnancy. I'll answer your question both ways.
Dogs don't always follow the rules so I would be prepared to get the male and female together several times for several breedings if you want to have a successful breeding.
It depends upon the dog but in general we see a bloody discharge during the first 5 to 10 days of heat, then a straw colored discharge with short period of fertility of 5 to 7 days, then the "going out of heat", although still attractive to males, period of 5 to 10 days.
So a heat cycle can be as short as a little over 2 weeks to almost a month. The fertile period is usually in the middle section when her discharge is straw colored or clear, after the bleeding stops.
In theory the initial part of her heat cycle with a bloody discharge (the first 5 to 10 days) isn't the fertile period.
The beginning of second part, just when her discharge becomes more straw colored, should be her fertile time.
If you want to be more precise have your veterinarian check vaginal swab cell cytology to see when she should be ready to breed. Your veterinarian can tell as her cell cytology changes when she is approaching her fertile period, when she should be fertile, and when it is too late.
Or you can have your veterinarian check LH hormone levels as she should ovulate a couple days after that spike. You would have to have her blood levels checked daily to find the spike.
The best way to tell when she fertile really is when she will stand to be bred. Hormones that are responsible for ovulation make her receptive to stand and be bred.
I do recommend that she visit the male's home and that she meet him daily if possible when you believe she is ready to be bred so you don't miss her fertile period.
Realize though that even with everything being done the right way she may not get pregnant.
If you are trying to avoid pregnancy that is where things get really tricky. She should only be fertile in the middle of her cycle, just after she stops showing an obviously blood tinged discharge. But I have known dogs to get pregnant at any point during the 3-4 week "heat cycle" period. That's because some dogs ovulate early, some late and sperm stays viable for a few days in her reproductive tract. Because of those things I tell owners as soon as they see vulvar swelling and a bloody discharge their pup is presumed to be fertile for the next month, and should be treated that way. She should never be alone, always go out on a leash in a fenced yard, and have no contact with males.
Best of luck either way, please let me know if you have any further questions.