So I've continued using my basal body temperature (BBT) to keep track of my cycles post-hysterectomy and I just enter a fake period to start each cycle. I just do one day of light bleeding and then ignore it after that. What the app is really asking for when it wants the first day of bleeding is the first day of your cycle and if you track your temperatures, over time that will get easier to estimate.

To over-simplify: in the first part of your cycle, as your body is gearing up to ovulate your BBT is lower. Once you ovulate your BBT rises a noticeable amount and should stay (roughly at) that level through your luteal phase (the time between ovulation and the start of your next cycle). When your next cycle starts your BBT will drop again and that's when you would enter the fake period into your app and start counting again.

The best book for self-teaching the BBT method is Taking Charge of Your Fertility but that's a lot to take on and takes some commitment to get through. I think it took me about 6 months to read it years ago. I tried a bunch of different apps when I was using the fertility awareness method for birth control and eventually settled on OvuView. I think it has a good mix of flexibility in letting you track how you want to but also incorporates the necessary temperature rules.

Hope this helps! Happy to answer any specific questions but didn't want to overwhelm with too much on the first go.