Bits are not numbered from right to left. They are numbered from lowest weight (the lowest weight bit getting the number 0 or 1 depending on the convention chosen) to highest weight (which can be 15 or 16, 31 or 32, 63 or 64, ...).
One reason to number them this way is so that the number of the bit number n that counts for 2n (in start-at-0 convention) will always be the same. If they were numbered in the other direction, the weight of bit n could not be inferred from n alone, it would also depend on the width of the word being discussed.
Another reason is that it is pretty intuitive to have bits with a lower number have less weight.
They end up being numbered from right to left when written because they are written from the highest weight on the left to the lowest weight on the right. Numbers have been written so for centuries. If this is what you are wondering about, the reasons have probably been lost but the Wikipedia page on the Hindu–Arabic numeral system may hold clues.