In this review, they define bidirectional transcription as:
Transcription that occurs on both the positive and negative strands of DNA simultaneously, where the direction of RNA polymerase progression along each strand is either is convergent or divergent.
How is that different from antisense transcripts? Is it that bidirectional transcripts don't need to overlap the nearby gene whereas antisense transcripts do?
Consider two RNA polymerases initiating on the same point of DNA, but on opposite strands. Transcription of each strand would occur, but the polymerases would be moving away from each other (divergent transcription), and the transcripts would not overlap. On the other hand, consider a polymerase initiating on a gene, and another polymerase initiating within the gene, but downstream of the transcription start site of the gene, and on the opposite strand. The polymerases would be moving towards each other (convergent) but transcribing opposite strands. Since the strands would be complimentary at points where the polymerases pass each other, this could give rise to antisense transcripts.