Combine first 4 ingredients in a medium bowl; stir in mayonnaise, lemon juice, and hot sauce. Cover and chill.
Meanwhile, cut peppers into 1 1/2" strips. (For bite-size pieces, cut strips in half crosswise.) Spoon crab filling onto pepper strips, and top with basil strips.
Make-Ahead: Cut peppers into strips and store in heavy-duty, zip-top plastic bags. Prepare crabmeat mixture 8 hours ahead. For a twist, top baguette slices with the crab mixture.