I am also a serious cyclist and have been having a hard time keeping fit. But running really helps and if you are a triathlete then you need to run anyway. I carry a duffel bag with all my running stuff on my trips and it works OK. Lots better than nothing.
I have seriously thought about getting a Bike Friday, but they are just way to ghey to reallly think about, even if they do ride nicely (from what I hear they are surprisingly good). But the fact is that logistically it is tough.
Best bet would be to live in domicile and bid trips where you can ride before you start and after you finish.
When I lived in Europe flying and riding was easier because the job consumed less of your life than it does in the US. But even there there were compromises.
Running is your best bet. Riding would not be impossible, but don't imagine it will be easy. Unfortunately.