"Be bested" refers to being defeated or outperformed by someone or something. There are a number of synonyms for this phrase that can be used to describe the same situation. To be "outdone," "outmatched," or "overpowered" are all ways of expressing the idea of being bested. Other synonyms might include "conquered," "vanquished," or "overwhelmed." Depending upon the context, some of these words may carry different connotations or degrees of seriousness. However, they all convey the same basic meaning of coming up short in a competition or challenge.