The dried "bitter" orange peel is supposed to be from Bitter Curacao Oranges. Fresh, they are very hard (read: almost impossible) to come by. The flavor and aroma of the cut up and dried whole peel (= pith and zest) we buy at the brew store is quite unique, unlike anything else. I'm willing to bet, very different than the fresh fruit would have yielded.
Without any problems, I've used who-knows-how-many-years-old-dried-bitter-orange-peel as you buy it in the brew store, then stored for many more years in a jar in my brew area. In dried state, the flavor carries on almost indefinitely.
Before adding them to the wort (or beer), I cut them up into much smaller pieces, and have even ground them in a coffee/spice mill. The smaller the pieces the larger the surface, the more, faster, and complete extraction you get. Merely minutes at the end of the boil or during whirlpooling.
Using fresh peel (or zest, without, or with various amounts of pith, depending on how deep you cut) from any citrus fruit will give you different flavors and aromas, each unique to their variety and origin.
For example, I brew a Red Grapefruit Saison that has a relatively large amount of fresh, whole red grapefruit peel in it (pith and zest), added to the whirlpool.