I think it's unlikely if it's covering your os. Potentially not impossible but you should probably assume that it's there to stay and then if there is movement then all the better. As you probably know, the placenta itself doesn't move - it merely 'stretches' up with the growing/expanding uterine wall which pulls it beyond the cervix. However, if it's covering the cervix then it's far less likely to be pulled up.
I'm currently on 'watch' for the position of my placenta. I had praevia with my twins and there's a possiblity I've got a low lying one again, which will be checked at my 20 week scan next week. My consultant said to try to imagine a plate sitting directly over your cervix - that's the reality of a covering placenta. One that's very low or partially touching will in all likelihood get pulled upwards as the uterus grows but one in a plate position is unlikely to as there's too much to move. Does that make sense?
As for bleeding, it's not a foregone conclusion. I had partial praevia (i.e. partially covering) that had moved to 'very close' by about 30 weeks but as I had two placentas in there (twins) the scope for movement was always limited. I bled very badly and spent the last month of pregnancy in hospital until I delivered at 35 weeks (not bad for twins I think), which is probably not what you want to hear but I also have a friend who had total praevia with her twin pregnancy and was warned of almost certain bleeding and didn't bleed a drop.
As for what you should be doing it's difficult to say. You can't influence the movement of the placenta unfortunately so there's nothing you can do on that score. However, there are things that are thought to increase the likelihood of bleeds occuring - namely exercise, sex, orgasms (the latter can irritate the uterus and trigger a bleed). Not all doctors/midwives advocate it but I certainly don't think it hurts, although it is crashingly dull. They tend to refer to it as 'pelvic rest' which sounds suitably boring. I found not having an orgasm the hardest part. Lack of sex was fine (hey, we can do other things I thought...) but not being able to have an orgasm was seriously annoying.
Final note if you do bleed then go to hospital. Even if it's not particularly a huge amount. Bleeding can trigger early labour (it irritates the uterus and can cause it to contract) which they can block with drugs.
I hope I haven't worried you. Lots of people have praevia with no bleeding at all but your chances are increased and although it's not the greatest news to hear I do think it's good to be prepared and have a mindset.
Feel free to ask any more questions.