A method of forming an asphalt mixture includes mixing a polyol with a bio-source material to form a bio-asphalt. The method can further include mixing the bio-asphalt with a bitumen source different from the bio-asphalt to form an asphalt mixture. The bio-source material can include an oil, such as a vegetable oil, an animal fat, or any combination thereof. The bitumen source can include a petroleum-based asphalt. The method can further include adding a modifier, such as a fatty acid, a polycarboxylic acid, a polyacrylic acid, a polyacrylate comprising a copolymer, or any combination thereof. Moreover, a roofing grade asphalt mixture includes a bio-asphalt. The bio-asphalt includes an alkyd, wherein the alkyd is a reaction product of a polyol and a bio-source material. The roofing grade asphalt mixture further includes a bitumen source material and particles.