Aspect Sentiment Triplet Extraction (ASTE) is a new fine-grained sentiment analysis task that aims to extract triplets of aspect terms, sentiments, and opinion terms from review sentences. Recently, span-level models achieve gratifying results on ASTE task by taking advantage of the predictions of all possible spans. Since all possible spans significantly increases the number of potential aspect and opinion candidates, it is crucial and challenging to efficiently extract the triplet elements among them. In this paper, we present a span-level bidirectional network which utilizes all possible spans as input and extracts triplets from spans bidirectionally. Specifically, we devise both the aspect decoder and opinion decoder to decode the span representations and extract triples from aspect-to-opinion and opinion-to-aspect directions. With these two decoders complementing with each other, the whole network can extract triplets from spans more comprehensively. Moreover, considering that mutual exclusion cannot be guaranteed between the spans, we design a similar span separation loss to facilitate the downstream task of distinguishing the correct span by expanding the KL divergence of similar spans during the training process; in the inference process, we adopt an inference strategy to remove conflicting triplets from the results base on their confidence scores. Experimental results show that our framework not only significantly outperforms state-of-the-art methods, but achieves better performance in predicting triplets with multi-token entities and extracting triplets in sentences contain multi-triplets.