Unfortunately I've got no good advises but I've read (just now) that you could send bitcoin from mars to earth (and vice versa) in less than an hour. But mining from mars would be hard (impossible?) because of the time it takes for the blocks to be broadcasted back to earth. Source: https://en.bitcoin.it/wiki/Bitcoin_in_the_far_future
Also for anyone who wants to learn more about possibilities mars economy: http://www.aleph.se/Trans/Tech/Space/mars.html
This is true, but not unbeatable. Currently Bitcoin is being broadcast on radio waves. Transferring it to the new tech of encoding data on waves of light, which is entirely possible with current technology, is probably the most feasible solution that is actually possible today
The current level of tech for encoded data transmission between celestial objects would have (with no interference) between a 2.5 and 21 minute transmission time, Earth <-> Mars, depending on the location of both planets. This is, of course, not taking into account objects like the Sun being between us