What mitigation can you do about the core problem (not what you want)?
This is a really tough situation given what you are asking. Nearly everyone you interact with at work is going to get this out of your request:
- "I can't control myself (sexually) around my female colleague and need to take fairly extreme actions to ensure nothing happens."
I would be just revealing my inappropriate line of thought
The problem here is YOU, not her. No matter what the reason (personal preference, religion, whatever) it is ultimately your responsibility.
I would suggest, among other things:
- Accept travel convenience. Avoiding the same flight/hotel/rental car is never going to come across well. I would accept that you are just going to have to deal with this aspect.
- Figure out some sort of accountability (or whatever) if you are worried about your actions/thoughts. Find a friend/spouse/whatever and touch base daily if needed. I don't know exactly what is driving this concern, but get a real person to touch base with.
- Avoid drinking 100%. Just don't drink alcohol on the trip, period. Get something else if your team goes out. Or whatever else they might do that causes your brain to go on vacation.
- Avoid 1/1 social gatherings. This will be hard and cost you some of your working relationship potentially, but just avoid doing 1/1 activities with your colleague. If traveling for work try to include others from your travel destination, too (easiest way to avoid 1/1). If you do social things try to have an early time to be back, if you are human your brain starts being more dumb the more tired you are.
- Identify the triggers for you feeling uncomfortable. Is it just interacting outside of work? Spending 1/1 time together? Having lots of time in the car? Etc. Once you figure these out you can find more specific and personal ways to address them. We can't know this and everyone is different.
- Journal/write in evenings. This is going to sound stupid perhaps, but take time to journal and process through whatever thoughts you have. Figure out what "stops them" and do them.
- Don't go into coworkers room. This seems obvious but it's not (I forgot it initially, thanks Bill!). If you need to coordinate in the hotel, stay in public areas.
Do what you can do to minimize your feeling of risk/whatever. But do absolutely everything you can to avoid those actions affecting your colleague.
Can you pull this off without destroying your career at this company?
Probably not easily.
That's not a good impression of you, obviously, and it's almost impossible to avoid coming across as sexist and discriminatory. Because it's pretty much exactly what you are doing.
Ultimately this is an entire tradeoff between how you want to be respected by your coworkers and how important this is to you.
There really is not a great way to phrase this, at all, except perhaps something like, "Out of respect for my spouse, I prefer to avoid situations other than work with women in a 1/1 context." Even this wording is going to be VERY controversial too among certain people, though, so keep this in mind.
How offensive is this?
Some people/coworkers might not care at all about such a request.
But those that do? You are really going to offend them.
That's why you need to carefully consider how important this is to you before doing so. I'm sure this question and comments/answers will show that, too..