Gentile female covering hair when meeting with orthodox men

I am a nurse who works in a very orthodox community. I am also a married female gentile of no specific faith. Many of my patients are also rabbis. I want to be respectful and do not want to cause my patients to stumble in their faith. Should I consider wearing a hair covering when meeting with orthodox patients, particularly men? Or would this be considered disrespectful seeing as I do not practice their faith?

Thanks for your question and may I show my admiration for your thoughtful show of consideration! There is no reason for a gentile to cover her hair, and it's actually better that they should know that you aren't Jewish. Nevertheless, if you wish, modest attire would definitely be appreciated, e.g. not too tight-fitting, and wearing at least 3/4 length sleeves, and a skirt (not pants) which at least covers your knees when sitting. It's not too difficult, and by doing so, both you, and they, will feel much (!) more comfortable and there will be a pleasant atmosphere of mutual accommodation and respect.