A man enlisting in the 10th Hussars in 1901 would have been given a number in the 5000s with each hussar regiment having their own sequence. If he transferred to another regiment he would have been renumbered. Between the Boer War and WW1 they seem to have enlisted all hussars into the Corps of Hussars with only one sequence. My guess is that 387 was such a Corps man, as the original 387 would have enlisted 20 or 30 years before your man. But you really need an expert in the numbering used by the hussar regiments.
The NA medal web site has a much better search facility than Ancestry, so you can search for hussars with number 38? to get their name, and then look on Ancestry for their record. This will tell you when they enlisted.
http://www.nationalarchives.gov.uk/documentsonline/browse-refine.asp?CatID=10&searchType=browserefine&pagenumber=1&query=*&queryType=1
For ‘institutions’ in the 1911 census the enumerator was only supposed to enter the man’s initials. So you need to look for A Rs as well. If he was married then it will be easier to look for his family, as the married quarters recorded full names. I am surprised you cannot tell the location. Have you checked all the returns and looked at the ‘district’ description?
Service before the age of 18 did not count, so he would have signed up until he was 30, ie c1915. So you would think he served in France. He may have purchased his discharge before WW1.
If you get stuck I would post a question on both the British Medal Forum and the Great War Forum, putting ‘10th Hussars’ in the title.
Ken