The phrase "have bearing on" means that something is relevant or significant to a particular issue or situation. There are several synonyms for this phrase that can be used in different contexts. For example, you can use the phrase "impact" to refer to something that significantly affects a situation. The word "influence" can also be used to convey a sense of importance or relevance. The phrase "be relevant to" can be used to indicate that something is related to a particular topic or issue. Similarly, "relate to" is another synonym that can be used to suggest a connection or correlation between two things. Ultimately, the choice of synonym to use will depend on the specific context and tone of the sentence.