밑밥's original meaning is a kind of bait in fishing. It means the food you throw into the water to attract fish to the area.
It also commonly refers to something people offer as a bait to push their agenda for attaining something bigger, usually in a bad sense. For example, we say XX 회원으로 행세하며 밑밥을 깔았다 or XX 멤버라는 밑밥을 깔았다 (They (falsely) acted like members of XX as a ploy).
So 그림에 조금씩 관심이 생겼다는 밑밥 probably means "a ploy/pretext that they got interested in painting", implying someone is using an interest in painting (which may not be true) as a bait to get something else they want (like getting a painter interested in them, for example). The person who said or wrote it saw through the ploy, because he or she wouldn't use the negative term 밑밥 otherwise.