It depends what you mean. If you are using the article 'the', you would say 'She jumps onto the bed'. This is because, when she lands, she will be ON the bed i.e. on top of it. In this situation, perhaps some children are playing in a bedroom and they are jumping from one piece of furniture to another. However, if you want to say that she went to bed very quickly i.e. that it was night time and she got under the covers very quickly and went to sleep, you would say 'She jumped into bed'. There is no article here, because you are talking about retiring for the night (going to bed) rather than bedroom furniture (the bed). And you would say 'into' because, when she had finished jumping, she would be 'in bed' i.e. under the covers.