If possible, I prefer to put my bike IN my car. That way, it is out of the elements and not covered in bugs or soaked by rain. If getting the bike in the car involves removing the rear wheel, be especially careful to protect the rear derailleur area from being bent. Do not pile other things on top of the bike frame.
When the inside of the car isn’t feasible, use a rack designed for your bike frame. Racks that clamp on the tubing are a very bad idea if your frame is made of carbon fiber. Rear-mount of roof-mount racks where the attachment point is the wheels are usually better with carbon frames. These are not foolproof though. I have seen forks break with the roof-top fork-mount racks.
The bottom line is that if you are able, put the bike IN the vehicle. When renting a vehicle, think about a minivan or other vehicle with plenty of space for your bike.
There are two ways to do this; One is to bring your bike with you and the other is to rent a bike at your destination. If your destination does not have rental bikes available, bringing your own bike may be the only option.
The pros of bringing your own bike are that it is a bike you are accustomed to with the accessories that you prefer. Also, you know it fits and is already set up well for you. You won’t need to worry about picking up or dropping off a rental bike and you will save the rental expense.
The cons are that you will need to rent or purchase a bike travel case and will likely need to pay a fee to the airline for transport. I have heard of fees as high as US$185 each way to bring your bike. There is also a risk of damage to your precious bike even with the bike case. This can be helped by packing the bike properly with frame dropout protectors installed. Don’t load a bunch of other stuff in with the bike. Soft bags are a gamble in my opinion. Baggage handlers do not love your bike as much as you do. You will need to rent a larger vehicle to accommodate your bike case or you will need to make sure that there is transport available to your hotel that can handle a bike case.
Renting is a good option if you plan well. You don’t need to worry about ruining your bike in transit. You won’t need to think about getting the bike to and from the airport.
You will need to plan ahead by having your bike fit coordinates on hand when you arrive. Also, it would be good to reserve a bike ahead of time in your size so you know you will have a bike waiting. The place you are renting from may or may not have the pedals, saddle and helmet you prefer, so bring whatever they don’t have. Don’t expect the rental store to do a complete fit for you. It is a far better idea to know exactly how your bike is set up and either adjust the fit yourself or have the shop do it if they are willing.
The cons of renting are that it won’t be exactly the bike you are accustomed to and of course it will cost you some money to rent. There may be a large deposit required so prepare for that. Ask when reserving what all the charges are and what deposit will be required. Ask if it is okay to swap pedals and saddle (if they say no, I wouldn’t rent from them) and also if there is a repair kit on the bike.
Whether you bring your bike or rent, bring along a pedal wrench, a bike pump with gauge, a tape measure and a multi-tool. Some old rags and chain lube are good to have as well.