I had complete plaventa pervia with DD.
Diagnosed at 32 weeks, straight to the consultant after the scan and given steroids. I was unlucky and had a bleed the very next day so back to hospital in the middle of the night. Very scary but luckily it stopped on its own accord.
Because I had had a bleed they wanted to keep me in hospital after that, but as I lived less than a mile away they let me go home, bit I was signed off work at that point.
DD was delivered at 36+1 after a second bleed. Again it had stopped on its own, but it was decided it would be better to deliver with no bleed in a controlled section early than a emergency second with uncontrolled bleeding. The section was very calm, DD was delivered without any issues and didn't need any help and just went with me to the recovery ward, so a good outcome after all the stress of the weeks before.
It is a scary scenario, but you can have placenta previa and it move up, or not bleed at all! I think they like it to be a few centimeters away from the cervix to allow you to attempt a natural birth.
I won't say not to worry because that is impossible advice, but know you will be looked after well.
Practical advice: Pack a hospital bag now, just in case, although hopefully you won't need it and plan how to get to hospital ASAP if you do have a bleed. Have some pads to hand as well. If you do bleed they'll want a look at how much blood you've lost.
Hopefully you'll need none of the above though and it'll shift. Do you knownof you have an anterior placenta? Apparently they are likely to move more.