It should be "bachelor's degree" with an apostrophe before the s, indicating possession.

graduate"s degree

You can write "bachelor's degree" using an apostrophe before the "s" in "bachelor's" to show possession. For example, "She earned a bachelor's degree in English literature."

newton gets its bachelor 's degree in physics h was educated in trinity , cambridge

They are quite often used interchangeably. However, on the degree document it is referred to as (for example) Bachelor of Arts. When individuals refer to the degree it is quite often indicated as a bachelor's degree.