I have a full bottle of orange flavored Bacardi rum-- any ideas for use?

You could make orange sorbet with a bit of it, using the rum instead of the triple sec or vodka in the recipe that I'll paste below. I like to layer it with vanilla ice cream like a creamsicle :)

Fresh Orange Sherbet by Cook's Illustrated

Published May 1, 2004.

Why this recipe works:

The perfect sherbet recipe is a cross between sorbet and ice cream, containing fruit, sugar, and dairy but no egg yolks. We found no need for extra ingredients such as egg whites, gelatin, and corn syrup in our sherbet recipe. For bright flavor, we processed fruit zest and sugar together in a food processor. We added some alcohol for smoothness and whipped heavy cream for a lighter texture, and prepared the sherbet in an ice cream maker to get an even texture.

Makes about 1 quart, serving 4 to 6

If using a canister-style ice cream machine, freeze the canister for at least 12 hours or, preferably, overnight. If the canister is not thoroughly frozen, the sherbet will not freeze beyond a slushy consistency. For the freshest, purest orange flavor, use freshly squeezed unpasteurized orange juice (either store-bought or juiced at home). Pasteurized fresh-squeezed juice makes an acceptable though noticeably less fresh-tasting sherbet. Do not use juice made from concentrate, which has a cooked and decidedly unfresh flavor.
Ingredients

1 tablespoon grated orange zest from 1 to 2 oranges
1 cup granulated sugar (7 ounces)
1/8 teaspoon table salt
2 cups orange juice, preferably unpasteurized fresh-squeezed (see note)
3 tablespoons lemon juice from 1 to 2 lemons
2 teaspoons Triple Sec or vodka
2/3 cup heavy cream

Instructions

1. Process zest, sugar, and salt in food processor until damp, ten to fifteen 1-second pulses. With machine running, add orange juice and lemon juice in slow, steady stream; continue to process until sugar is fully dissolved, about 1 minute. Strain mixture through nonreactive fine-mesh strainer into medium bowl; stir in Triple Sec, then cover with plastic wrap and chill in freezer until very cold, about 40 degrees, 30 to 60 minutes. (Alternatively, set bowl over larger bowl containing ice water.) Do not let mixture freeze.

2. When mixture is cold, using whisk, whip cream in medium bowl until soft peaks form. Whisking constantly, add juice mixture in steady stream, pouring against edge of bowl. Immediately start ice cream machine and add juice/cream mixture to canister; churn until sherbet has texture of soft-serve ice cream, 25 to 30 minutes.

3. Remove canister from machine and transfer sherbet to storage container; press plastic wrap directly against surface of sherbet and freeze until firm, at least 3 hours. (Can be wrapped well in plastic wrap and frozen for up to one week.) To serve, let sherbet stand at room temperature until slightly softened and instant-read thermometer inserted into sherbet registers 12 to 15 degrees.

If you're still looking for cocktails or punch, 2 classic drinks that already have rum and orange in them are Long Island Iced Tea and Mai Tai...you could use the orange Bacardi in one of those.
Or make an orange variation on a mojito (omit the lime juice & lime garnish).
Or search sites like Epicurious, allrecipes and some drinks recipe sites that allow search-by-ingredient and search-by-what-I-want-to-omit.

Chocolate orange rum balls, I make fruit cake for the holidays and use rum sometimes for the soaking syrup it would be nice for that if you make fruit cake, if not any boozy cake that calls for a soaking syrup would be nice.

One of my favorite non alcoholic punches for summer events is oj, pineapple juice with a splash of cranberry. Maybe do that with your rum? Might be a festive summer drink. Almost a mai tai minus the Myers dark rum.

Send it to the person who was looking for a drink to ease their cold?