counter for parts, stages, installments
Used especially in the pattern 第〜弾 (e.g., 第２弾) for numbered installments of a series, project, or campaign.
The third installment of the popular series will be released next month.
counter for bullets
Counts bullets, shells, or similar projectiles. Less common than 発 (はつ) in everyday speech.
The criminal had loaded six bullets into the handgun.
The second installment of this campaign starts next month.
As the first phase of the new product, we released a smartphone app.
One of the shots hit the target.
発 is the standard, everyday counter for bullets and shots, while 弾 is a less common alternative used in the same role.
回 is a general counter for occurrences or times, whereas 弾 specifically counts numbered installments or stages of a series, as in 第２弾.
From the kanji 弾, originally meaning 'bullet' or 'projectile'. The counter use for installments likely developed from the idea of 'firing off' parts of a series.