For me the one I believe to be correct is where the person goes on holiday and does the same things they do at home just in another place, so no real holiday.

I like this one:

There are a few different theories on the origin of the phrase "busman's holiday". The version most commonly accepted hearkens back to the horse-driven omnibuses of 19th Century England. The drivers of these omnibuses often grew very attached to their particular team of horses pulling their carriage through town. During their days off, many of these omnibus drivers would disguise themselves as regular passengers in order to keep a critical eye on the relief drivers and the horses. It is said that the phrase "busman's holiday" arose from this practice of bus drivers spending their downtime riding the buses.

http://www.wisegeek.com/what-is-a-busmans-holiday.htm

I go quite a way along with Mrs Too's answer but I had always heard the following when I was small from my dad...

Back when HE was a lad whic'll be early 1099s, the only transport to use when going on a holiday was a bus.

So, a busman ie a bus driver going by bus on his own free time was just doing what he did for the other 50 weeks of the year.

No holiday at all - which explains the expression.