You calculate how far along you are based off your last menstrual period (lmp) and the only way to make it more exact is an ultrasound. If dr uses ultrasound to date then ask when conception would have occurred.
And If you look up conception calculator online you can enter your due date and it will give you the possible conception range.
Fyi...your mid cycle bleeding might have been ovulation or implantation spotting.
Is this just a matter of curiosity, or are you trying to determine paternity? If the latter, see if you can get an ultrasound as soon as possible, and ask them for an estimated due date. From that date you can compute an estimated conception date.