You can add -지만 to present, past and future form. 바쁘다 is an adjective(state verb). present - 바쁘지만 past - 바빴지만 remote past - 바빴었지만 future - 바쁘겠지만

yes, it is an accurate representation past form of verbs can come. ex) present tense : "바빴지만", past tense : "바빴었지만" another ex) an adjective,it also can come present tense : I am tired but - 피곤하지만 past tense : I am tired but - 피곤했지만