I could not find any. I am afraid one of the explanations for this is a number of constructs you are willing to explore. With every addition it is getting more difficult. I could not find flicking through online content for burden of travel questionnaire and you would like to get this for patients in rural areas so it is making the case even more difficult.
I am afraid you may need to consider designing such a scale. The good news is you could get citations as the author of such an instrument.
I think, you are the best person to develop a questionnaire of your own which will serve the purpose best, because you know
1. The type of ailment of your patient
2. Distance and time from the patient's residence and hospital
3. Availability and mode of transport
4. Terrain and climatic condition of the study area
5. Condition of road / railway / Water-way etc.
6. Socio-economic condition of the patient
7. Cultural belief and the social taboo of the patient's family
These are the few parameters which you should consider to develop your questionnaire.
In case of Natural, Quasi-natural or man-made calamities burden of travel increases. So you can develop a special section in your questionnaire which will be useful in those days.