If you are talking zoology, then there are opportunities for travel, but be aware the jobs are not about travelling - travelling is a means to get to the research sites. So head for research/conservation research, specialise in tropical species/species found outside the US and you'll travel - but you'll be travelling in economy and living in field camps. It's tough. You either enjoy that kind of thing, or you don't. Select a university with lecturers with a good background in animal behaviour and learn - those types of jobs are much sought after, and it will be a long hard slog - you need to have a good background, and you need to have good contacts who are willing to champion you with their contacts - it's a competitive field, most biologists want to do field based research overseas. I'm UK based, and your first degree wouldn't be so important (except to get a good solid base, and build up your contacts), it's your PhD/Doctorate you would be really looking to do outside of the US - but you would end up living wherever your subject was (an example, I applied for a PhD in Mongolia, researching antelopes, which would have meant living in tents in Mongolia for a a lot of the time). Volunteer for stuff outside the US - one of my students wanted to get into marine research, and ended up in Australia and Oregon, volunteering with projects which gave her experience in the field which made her CV delectable, but which she had to self fund. But that experience got her her PhD on grey seals so she's now set for the field she wanted to work in.

Another option would be to aim for one of the major international conservation organisations - but be aware a lot of them are based in Europe (I'm thinking bodies like the IUCN, Birdlife International etc), and so you might not be eligible to work for them. As an international body, there would be opportunities for travel, but likely in economy, since most of them run their budgets on a shoestring. As someone who flew a lot in longhaul Y for work - it's overrated

Your final option is the one I ended up in accidentally. Consultancy. However, international travel can be unusual, most environmental consultants are limited to travel within their own country - unless they have skills which are so rare and so unusual that people will pay them to fly in. By definition, it's hard to find a specialism like that, and the downside of that is that it can also leave you too specialised as well.

In the US, you could also end up going for a wildlife biologist role, which may involve some national travel, but with the possibility of international conferences.

Ultimately, as a zoologist from the US, looking for the job in which you fly in from the US and then fly out again, be aware that it will nearly always be cheaper to employ a local scientist, who is likely just as skilled as you are, and has more awareness of the local species and/or laws, than to fly you in from the US, unless you become specialised and/or a recognised expert. There are opportunities for travel, if you go into field research, but you have to be aware that they (typically) won't involve much in the way of comfort or mod cons. And if you are squeamish - you should be aware that all field biology involves getting your hands dirty at some point. Whether it be destroying injured animals, gathering up pooh samples, spending two weeks on a boat with a dozen men and no onboard toilet (as one of my female lecturers did!), you just can't be squeamish as a field biologist.

Sorry to be a bit negative, but it seems like your expectations may be a bit unrealistic. However, there are jobs in the field which do involve travel, you might just have to adjust your expectations. OTOH - if any of this is what floats your boat, then I know a lot of my colleagues get a lot of fulfilment out of living in basic conditions but really getting to know the subjects they are working on, or working hard to conserve species which are on the brink of extinction. For many biologists that kind of thing is the dream job (and so, lots of competition!).

If you have any questions, then feel free to drop me a PM.

Oh yes, and if you don't speak any other languages, start learning. Being able to get by in non-English speaking countries will be a real plus.