Spoon a thin layer of peanut butter on top of each banana slice. Insert a toothpick through the peanut butter layer into the banana. Place banana bites onto the prepared baking sheet; freeze for 30 minutes to overnight.
Melt chocolate and oil in the top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching.
Place butterscotch lollies in a food processor, process until chopped finely. Cover another baking sheet with waxed paper.
Remove 2 to 4 banana bites from the freezer at a time; coat each bite with chocolate mixture. Place coated banana bites on the second baking sheet; sprinkle each with butterscotch bits . Repeat until all the bites are coated. Return banana bites to freezer until set, at least 1 hour. Allow bites to sit in room temperature for about 15 minutes before serving.