{Bill does a lot more exploring than Lanette. This is even a little canon. There are not only his exploration logs in LGPE, but at least in PokéSpec and Electric Tales, he’s been known to travel to do field research. Which is difficult to consolidate into his character because the anime and GSC also establish that he intends on sticking around his home for science and that he doesn’t like going outside anyway, respectively, but hey. I like to play that off as just talk.
In terms of the canon of this blog, absolutely, Bill will travel to the ends of the earth to follow leads about new pokémon, new talent for the system, or just scientifically interesting things in general, or he’ll be asked to swing by other regions to offer his assistance and expertise to other researchers and engineers. He still spends a lot of his time in the Sea Cottage performing experiments or in Goldenrod, seeing his family, but, you know. That’s probably like two-thirds of the year.
As for Lanette, she’s a bit less adventurous and more work-oriented/dedicated to the system itself. She’ll absolutely be sent places for work (especially if Bill can’t go or can’t be arsed to go himself, as in the case of anything involving Unova), and if Bill invites her along, she absolutely will go with him to meet new admins or to follow leads on adventures. It’s just that she’s a little less adventurous/curious, which means that she might check out the Regis’ chambers or reports of the Mirage islands, but she’s much less likely to do so without studying them thoroughly, weighing the pros and cons of going, stocking up, and very likely getting someone else to go with her. Or in other words, she’ll go exploring; it’s just that she’s often less … impulsive about it.
(Well, that and she doesn’t get paid nearly as much and can’t sweet-talk her way into getting a grant for anything, as Bill apparently does and can. Dude probably didn’t even have to pay for half the materials in his lab or the time he’d lost by getting stuck as various pokémon.)}