Roast the bell pepper over a gas flame or under a preheated broiler, turning occasionally, until charred all over. Transfer to a plate to cool. Discard the skin, stem and seeds. Coarsely chop the pepper and transfer to a blender. Add the mayonnaise, anchovies, mustard, lemon juice, garlic and saffron and puree. With the machine on, add the oil. Season with salt, pepper and Tabasco; serve.
The rouille can be covered and refrigerated overnight. Bring to room temperature before serving.