Video question answering (VideoQA) is a complex task that requires diverse multimodal data for training. Manual annotation of question and answers for videos, however, is tedious and prohibits scalability. To tackle this problem, recent methods consider zero-shot settings with no manual annotation of visual question-answer. In particular, a promising approach adapts frozen autoregressive language models pretrained on Web-scale text-only data to multi-modal inputs. In contrast, we here build on frozen bidirectional language models (BiLM) and show that such an approach provides a stronger and cheaper alternative for zero-shot VideoQA. In particular, (i) we combine visual inputs with the frozen BiLM using light trainable modules, (ii) we train such modules using Web-scraped multi-modal data, and finally (iii) we perform zero-shot VideoQA inference through masked language modeling, where the masked text is the answer to a given question. Our proposed approach, FrozenBiLM, outperforms the state of the art in zero-shot VideoQA by a significant margin on a variety of datasets, including LSMDC-FiB, iVQA, MSRVTT-QA, MSVD-QA, ActivityNet-QA, TGIF-FrameQA, How2QA and TVQA. It also demonstrates competitive performance in the few-shot and fully-supervised setting.