We went last year with 4 people and 3 bikes – ended up renting a Chevy Suburban, which is the biggest SUV you can get I think. We could fit the bike bags in stood up in the boot length ways. Anything smaller we would have seriously struggled. Previously we’ve used a Chevy Tahoe (Ford Expedition) and that would have been too small – it essentially the same car but with a shorter boot.
The American SUV’s are huge on the outside but not actually that big on the inside.
You’ve only got 2 bikes – so you may be able to get away with smaller.
You can get the boot dimensions on the internet of the various cars and then check if the bike bags fit.