Scene Text Recognition (STR) is the problem of recognizing the correct word or character sequence in a cropped word image. To obtain more robust output sequences, the notion of bidirectional STR has been introduced. So far, bidirectional STRs have been implemented by using two separate decoders; one for left-to-right decoding and one for right-to-left. Having two separate decoders for almost the same task with the same output space is undesirable from a computational and optimization point of view. We introduce the Bidirectional Scene Text Transformer (Bi-STET), a novel bidirectional STR method with a single decoder for bidirectional text decoding. With its single decoder, Bi-STET outperforms methods that apply bidirectional decoding by using two separate decoders while also being more efficient than those methods, Furthermore, we achieve or beat state-of-the-art (SOTA) methods on all STR benchmarks with Bi-STET. Finally, we provide analyzes and insights into the performance of Bi-STET.