If you have all the bones and a familiar/runner to help you bring as many bones to the altar as possible, you could get it done in anywhere as little as 3-4 days, to as long as 2-3 weeks. It just all depends on how much you play obviously.
The bottom line though is that training prayer on a Gilded Altar with Frost Dragon bones hardly takes any time at all
If you no life, it'll take you about a week. Try to bring a familiar and have the hometabs and such ready so you can do runs as quick as possible to save time.
I assume that you are buying Frosties though, for the fastest exp possible. If you can afford it, then definitely go for it! Unfortunately I could not afford Frosties and so I stocked up on infernal ashes immediately after bonus exp weekend in September... but the advantage was that I was able to buy enough to get me from 74-95 prayer for only 70M!
Mind you, I did have to run an extra 5k ashes that would not have been necessary if I went with Dragon bones instead. But even going the route of D bones costed a ridiculous nearly 20M extra. Thank god for the bonus exp market