There are several synonyms that can be used in place of "drew up on". One could use "approached", "pulled alongside", "pulled up to", or "caught up with". Each of these phrases refers to the act of closing distance between two objects, such as a vehicle or a person. "Approached" simply means to come near, while "pulled alongside" implies that the two objects are moving parallel to one another. "Pulled up to" and "caught up with" both suggest that one object was behind and is now even with the other. No matter which phrase is used, they all describe a similar situation of two objects drawing nearer to each other.