Bumping, voluntary or involuntary can happen on any cruise. There is a major difference between a ship being oversold and a customer being bumped because of a full ship charter. With an oversold ship the cruise line will, almost always, offer incentives to people in order for them to book another cruise or sail on another ship that leaves at the same time.
Here is Royal Caribbean's policy:
Carrier may for any reason, at any time and without prior notice, cancel, advance,
postpone or deviate from any scheduled sailing or port of call, or substitute another vessel
or port of call, and shall not be liable for any loss whatsoever to Passenger by reason of
such cancellation, advancement, postponement, substitution or deviation.
On a full ship charter the cruise line has already received a large sum of money and really isn't "that" interested in offering to give people extra money or other compensation in order to have them sail on another cruise.
If the ship is overbooked the cruise line will, most likely, offer you an incentive, of some sort, to cancel and go on another cruise. A common incentive is: A full refund and XX% off your next cruise. If the incentive isn't good enough for you then hold out for more or take the cruise.
If the ship is "chartered" by a private group all the cruise line is required to give you is the money you paid the cruise line for your cruise. If the cruise is six months away, or less, the cruise line will "usually" offer some sort of additional compensation. If it is a year out then you may only receive your cruise fare.
Full ship charters are a big money maker for cruise lines and they will gladly charter out an entire ship, especially during off peak times, rather than having to cut fares, as the cruise approaches, in order to fill the ship. A less than full ship is not good for the bottom line.
Some things that you may want to know about bumping.
1. "Almost" all travel insurances will NOT compensate you for your cruise fare. The cruise line refunds this amount and the travel insurance company will not give you a windfall profit because of it. You would basically receive twice the amount of the cruise price if they did.
2. Travel insurance will pay for your, unused, non-refundable airfare in the event you are bumped, BUT if the airline gives you a credit, that you can use at a later date, the insurance company will deduct that credit from the total cost of the airfare.
3. If you are bumped the cruise line will not refund your airfare unless you purchased the airfare through the cruiseline.
4. A full ship charter is "more likely" to happen on a smaller ship than a large one. There are very few groups, other than a "Rosie" cruise, that can fill a 3,000 passenger ship.
5. Charters usually occur 9-12 months before the sailing date.
6. The cruise contract expressly reads that the cruise line may cancel your cruise and you will be refunded your cruise fare or deposit. That's all.
7. All cruise lines have bumped or given incentives for people willing to cancel their cruise because the ship was oversold.
8. The most notable cruise lines for canceling cruises because the ship was chartered by a private group are: Holland America, Seaborne, Royal Caribbean and NCL.
The good news is: Both, bumping and canceling occur but they ARE NOT the norm so your chances of being bumped or your ship being chartered out from under you are small.