Yes ,you can use questionnaires with open-ended items to collect data from busy Doctors,but chances are that you will achieve a very low response rate.One method i have found to be very effective when are collecting data from  busy subjects is Free-thought listing, where you ask the research participants to list their thoughts about the subject under investigation on a prescribed form.,Thought listing forms can be completed in less than five minutes.However, this method is most productive  in  perceptions and opinions based studies and is not suitable for collecting structured data.

Video ethnography coupled with content analysis-not so much the best but a triangulated method that is least disruptive yet comprehensive enough.

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For very busy persons, you may want to try an Expert Panel Discussion or a Mini Delphi Approach

You might also talk to the people who manage their schedules to find out if there are times when are more available, such as the lunch hour.

For very busy person I think you would to aplly interview by phone.

 Thank you for the answers. Every answer seems to open up new ideas .

To a large extent, your philosophy, epistemology and ontology will "guide" the methods, techniques and strategies that are best deployed for achieving the objectives of your study. So will your research question(s). Do you want to approach the study with a pre-existing theoretical framework, or does your research question have very little prior theory in the published literature such that you need to "discover" theory that is "grounded" in the data? In my opinion, you need to iron out these preliminary issues first, before you decide on the workable methods, techniques & strategies for data collection.

https://www2.le.ac.uk/colleges/ssah/documents/research-training-presentations/EpistFeb10.pdf

http://www.walesdtc.ac.uk/conference/programme/how-to-get-clear-about-method-methodology-epistemology-and-ontology-once-and-for-all/

I second what Anthony says.  Your research question(s) and qualitative methodology need to drive your approach to data collection.

For busy doctors with limited time, try a diary-method. Let them log their daily activities that you later on can sort and analyze qualitatively. Do follow-up telephone interviews after a certain amount of time (lets say on a weekly basis). 

You need to decide ahead of time which qualitative design or approach you want. Then use different data collection strategies. Incorporate online questions, social media like whatsapp and facebook messengers and email. These can generate data in a timely manner since they can reply to your questions at their free time. But make sure confidentiality measures are put in place!!!

As your questions is formulated I would suggest a participant observational studie; just because they are busy. So, just follow them in their daily work.

I am coming to this a tad late Frincy. Here's my experience: I conducted face-to-face interviews with GPs (General Practitioners) across a number of states in Australia either in the Residential Aged Care Facility they were working in or their GP Clinic. I note that someone has answered- "look at their schedule and work around that" - this can be done. In some cases the GPs requested to see the types of questions in advance...no problem. Its purposeful sampling so there are no surprises....[what I am describing is published].