Not permanently change the line, but just occasionally, like how Mark would sometimes say "You can take the girl out of Jersey, but you can't take the Jersey out of the girl" instead of Hicksville. You're aware that's down to geography, and not personal preference, right? In NY, it's always been sung as Hicksville, but because the audiences at touring venues are unlikely to know that Hicksville is a town rather than an abstract concept, they change it to Jersey for other productions. Hicksville the town is quite different from Hicksville the concept.
I always liked the stories of various casts getting to lines about George Bush and being greeted by stony silence by the large groups from Texas that occasionally show up. (It occurs to me that that's definitely a 'Dirty Rotten Scoundrels' story but I'm sure similar must have happened at 'Avenue Q' over the years.)
Why do you find it hard to believe that Brits would find that as hilarious as US audiences? I like to think we're pretty big on political satire here, and I've always been able to find Brits more willing to stand up and be dismissive of world leaders than Americans. Just because we didn't choose Bush doesn't mean he doesn't have a big effect on us.
Part of me really likes the idea of keeping the Bush line intact. It scans, and I imagine the memories of 'Avenue Q' will fade LONG before the memories of the Bush administration. But I always thought they were going to change it when the time was right. We'll find out in a few months, anyway!