The buses don't have seat belts so you can't use car seats on them.
When flying, you can gate or baggage check your car seat and most airlines do not count a car seat or stroller against your baggage count because they are assistive devices. I also believe that gate checking a car seat is a bit safer because these items are loaded last with the wheel chairs. You can put it in a bag but it's not required. A bag will only prevent it from getting dirty (and it may be easier to carry thru the airport in a bag as well). Airlines also consider car seats and strollers to be fragile objects and will not reimburse if they are lost or damaged.
I will never rent a car seat for a couple of reasons: first, there is no way to know the history of a rental seat, ie whether it's been in an accident, how it's cared for, plus rental seats often don't come with the manual and if it's a seat you're not familiar with, w/out the manual you won't know if you're using it according to mfgr directions or not(remember 80% or more of all car seats are improperly installed). OK maybe that was more than two reasons right there

lol. Also, you can spend about $10 a day to rent a seat so it's just not cost effective if you're spending a whole week or more somewhere (and we personally never go to DW for less than a week). Oh, one more reason: car rental agencies do NOT guarantee they will have the seat you requested.
I wouldn't buy a seat at a vacation spot unless I had to. I just feel much more comfortable using our own seat that we are familiar with.
hth