Unfortunately underwriters don't see it that way. In order to get the best, (cheapest), deal possible companies accept restrictions and exclusions.
As far as the company is concerned you are on a layover, in the company's time and it is your duty to be properly rested and fit for your next duty. I'm being devil's advocate here, by the way. Your company will have an insurance department, so it wouldn't hurt to check what limitations there are on the policy they hold on staff when they are on duty and away from base, expect skydiving and white-water rafting to be excluded!.
That said I doubt if hiring a MC is excluded provided it isn't categorised as a high performance or 'special'. Be sure to have a helmet, irrespective of the law, from an insurance point of view, if you are injured, sans helmet, you are likely to be considered 50% responsible for and therefore 50% liable for cost of your own medical problems! (Same as not wearing a seat belt in a car). Possibly the hirer can sell you a personal accident policy, with medical costs included, to cover the period of the hire, go for a high policy limit.
Sorry to be all doom and gloom, I enjoyed a good time down route as much as the next person but you would be surprised how many people don't give a second thought to any of the possibilities and ramifications if things don't go as planned, they are injured and now can't operate their roster and may have a whopping great bill to pay! (It is called being in Deep Sh*t!).