Bellatrix was demented, evil and cunning, but she didn’t delve as far into the dark arts as Voldemort did. It cost Voldemort every time he made a Horcrux. Bella knew how to make one, most likely. Her beloved Lord and leader would have explained it to her at dinner one night, and she kept one of his Horcruxes safely in her vault at Gringotts.
But Bellatrix Lestrange, as awful as she was, didn’t want to ruin her body and face by creating a Horcrux. She had no trouble hurting and killing. She killed Sirius Black and seemed to thoroughly enjoy it. But I don’t think she wanted to go down the black path of her Lord. She saw his fall when he tried to kill the baby Harry Potter. Bella didn’t want to try for immortality. Bellatrix felt comfortable being one of Voldemort's most trusted servants. She felt that serving him was enough for her. She sought out nothing other than pleasing Voldemort, and somehow, I don’t think Voldy would have been thrilled to discover his followers were creating Horcruxes, so they too could live forever. No, the man would have gone mental had anyone else tried and succeeded. Horcruxes were his domain and no one else’s.
Remember that Voldemort always thought of himself as very unique and special, able to create things and take magic where it had never gone before. He plumbed the depths of dark magic. He flew unaided. He killed many times. Bellatrix was a very loyal follower. She even screamed at her trial that she would eagerly wait for the Dark Lord’s return. And he did return. Bella was willing to go far to serve Voldemort, but she was smart enough to not try and be as powerful as he was. Bellatrix understood Voldemort for the most part, so she stayed away from Horcruxes. At least, she stayed away from making any for her.
Potter, you cannot win against me! I was and am the Dark Lord's most loyal servant. I learned the Dark Arts from him, and I know spells of such power that you, pathetic little boy, can never hope to compete!" —Bellatrix regarding her own loyalty and skill
Bellatrix may not have been into immortality, but she certainly was into self-preservation.