A colloquial phrase used to change the subject or to introduce something abruptly with no lead-in; similar to 'This is sudden, but...' or 'By the way...' in English.
突然だけど、来週末に引っ越すことになったんだ。
This is sudden, but I've decided to move next weekend.
突然だけど、今夜ご飯を一緒にどう？
This may be sudden, but do you want to have dinner together tonight?
突然だけど、ちょっと相談があるんだ。
This is abrupt, but I have something to ask you about.
突然だけど、その服すごく似合ってるよ。
Randomly, but that outfit really suits you.