"네가 바쁘다고 우리는 추측했어."
Translation:We guessed you were busy.
Worth checking. My impression is:
1 ~다 고~: declarative statement. In this case, Speaker makes a wild guess (assessment without evidence)
e.g: I (/he/she etc) assumed that you (we/they etc.) were busy.
I thought that the shoes were quite expensive
2 ~나 봐: comment expressing the speaker's impression of a situation.
e.g. You seemed busy. (speaker's impression)
The shoes looked expensive. (in speaker's opinion)