I have seen others with bikes and others with golf clubs but make it clear when booking you want to do this and best check which ever airline you are going with that they will accept your bike, don't think this should be a problem though, but worth checking.
The obvious answer is to ask P&O since they are ultimately the ones who are going to give you permission to take the bike or not. I don't see that it is any different from any other piece of luggage really? Having said that, you may have to keep it with you in your cabin! You are obviously a very fit 70 year old lady Mrs Cole? Is this your answer to saving money on P&O tours? Happy cruising.