The Poskim discuss whether a blessing may be recited over cologne or perfume. Rabbi Ovadia Yosef (Hazon Ovadia, Berachot, pg 313) explains that one may recite a blessing before smelling a synthetic product which produces a pleasant smell, and the blessing would be “Bore Mine Besamim”. Rabbi Pinchas Scheinberg (quoted in Vezot Haberacha, pg. 175), Rabbi Ben Zion Abba Shaul (Or LeZion, vol. II, ch. 14:38) and Rabbi Moshe Levi (Birkat Hashem, pg 525) all agree with this position as long as one is smelling from a bottle and not from one’s hand or body, since the fragrance is considered to have already dissipated. Rabbi Shalom Elyashiv and Rabbi Shlomo Zalman Auerbach (also quoted in Vezot Haberacha) are not certain that a blessing may be recited over perfume or cologne because it is considered an unsubstantial fragrance and one that has been processed to the point in which it is no longer related to its original source (cf. Orah Haim 216:6). As such, they say that one should not recite a blessing over cologne or perfume. Interestingly, Rabbi David Yosef (Halacha Berura, vol. XI, § 216) concludes that one should not make a blessing and that indeed his father, Rabbi Ovadia Yosef agreed with his opinion, contrary to what he had written.
Summary: There is a Halachic basis to rely upon if one wishes to recite “Bore Mine Besamim” before smelling perfume or cologne from the bottle.