When you are writing phrases like “bachelor’s degree,” “master of arts degree” and “doctor of philosophy degree” use all lower-case spelling. Less formally, these are often abbreviated to “bachelor’s,” “master’s,” and “doctorate”: “I earned my master’s at Washington State University.”
The only time to capitalize the spelled-out forms of degree names is when you are specifying a particular degree’s name: “Master of English Composition.” However, the abbreviations BA, MA, and PhD are all capitalized. In modern usage periods are not usually added.
Be careful not to omit the apostrophes where needed. Some schools have adopted a spelling of “Masters” without an apostrophe, and if you work for one of them you may have to adopt this non-standard form for institutional work; but usage guides uniformly recommend the apostrophe.