If I was looking for alcoholic beverages, the first place I would check is the bar, meaning the Dugout Inn or the Third Rail.
However, the exact contents of their stock is random. Since you're looking for Rum and Bourbon specifically, and for a specific use for which you only need one or two, I checked the wiki pages for permanent locations, and found this:
- Whitechapel Charlie always has some for sale.
- Cabot House will have stored bourdon bottles in cabinets.
- In the basement refrigerator of the Cabot House.
- On the Prydwen, in the briefing room.
- In the basement of the D.B. Technical High School.
- Off the cliff south of Fort Strong, floating in a cardboard box with a teddy bear.
- At an unmarked, demolished swamp town south of Gunners plaza, floating in a cardboard box with a 2 teddy bears. Box is inside the ruins of a house with a red dog house next to it and just east of a house with green siding with the rear wall missing. Warning: 2 or 3 Yao Gaui's may be present at this green-sided house.
- Inside Joe's Spuckies near Postal Square.
- Behind a book shelf in the Croup Manor basement.
- On a boat just north of Pickman Gallery, in a cardboard box with a teddy bear.