When used as a suffix, the voiced form of 振（ふ）り ‘style’, 振（ぶ）り will be used to indicate either the way something appears, or some specific lapse of time since the last time something happened. This can be translated as ‘for the first time in (A)’, or ‘haven’t done (B) for (A) time’.
As ぶり (appearing most often in hiragana) is a suffix, it will be used after nouns. When followed by に, the part (B) portion of the sentence will give more information about what wasn't done for the period of (A). Additionally, ぶり may be followed by の when attached directly to a second noun that is being modified by ぶり.

• 1年（ねん）ぶりに５キロも走（はし）ったから明日（あした）は絶対（ぜったい）に筋肉痛（きんにくつう）だ。
  I am definitely going to be sore tomorrow because I ran a 5K for the first time in a year.
• 3年（ねん）ぶりに風呂（ふろ）に入（はい）る。
  I bathed for the first time in 3 years.
• 4年（ねん）ぶりの寿司（すし）だ！やっぱり日本（にほん）の寿司（すし）はうまいな！
  This is my first sushi in 4 years! Man, Japanese sushi is the best!
• 高橋（たかはし）選手（せんしゅ）が10年（ねん）ぶりの優勝（ゆうしょう）！
  Takahashi won for the first time in 10 years!