I can't say much about the blood test since the blood test would pick up HCG before an HPT would but, I know that if what you had was implantation then the blood test wouldn't have picked up any HCG either cuz the baby hadn't implanted yet. I don't know what brand of test you used when you got faint BFPs but they could've been evaps especially if they were blue dye. And what could be happening right now is that you got a dip in your chart when you started the bleeding cuz it could've been implantation. This is what happened to me with my son. My temp was 97.77 and the next day it dropped down to 97.25 and I started spotting a tan color. I was 12dpo when it started. Then, the next day it went up slightly to 97.27 and the spotting continued for 5 days. The day after that it went back up to 97.77 and stayed elevated which showed me I had implantation. I did take 2 Answer tests at 12dpo when the spotting started and I got extremely faint lines. Then at 16dpo, when the implantation ended, I took 2 Clearblue's and I got extremely faint positives so I took a digi and it was negative. So, I thought I had a weird AF, I wasn't pregnant and that was that. But I had an extra digital that I decided to take at 18dpo and to my surprise it was a positive. It was confirmed later on that day. I was 3 weeks and 3 days pregnant.
It's very possible what you had was implantation, especially cuz of the dip in your chart. The blood test would've been negative anyway until implantation occurred. So, I'd test again and if you're still unsure, go for another blood test.
I hope this helped! g/l