Just a little bit of explicit unconfusion. The bit order always appears to be high bit first inside the cpu. That is, "left-shift" always doubles the value and "right-shift" always halves it which implies that the high bit is on the "left".  Bit-order can matter in serial transmissions, but only at very low levels.
order which is visible to application software and that's what the above answers are about (as, indeed, they say).  Sometimes, books which deal with both (eg, books on networking protocols), will use "msb" for most significant bit and "MSB" for most significant byte.