I had spotting around the time my period was due with my son. It was brown spotting though. I was on vacation at the time and didn't get it checked out till 2 weeks later or more, but my baby was fine.
With my daughter however, it was an actual bleed and not at the time my period was due. I already had a BFP at around 15 or 16 DPO but started bleeding bright red at around 6 weeks pregnant. I was bleeding on and off that pregnancy until around 16 weeks.