So, I'm currently eating about 1800 kcal as I'm cutting. I intend to start bulking next week and I should eat about 3300 kcal for that.
My question is, should I increase slowly the calories or do it at once? If slowly, how much? 500 kcal per week till I hit the 3300?
If you've been at a deficit for an extended period of time, yes add slowly to avoid excess fat gain. Adding 300-500 a week is probably fine.