There are fanfictions where Bickslow and Lucy start off not getting along very well. But as they are forced to work together on various missions, they begin to understand each other better. Bickslow realizes Lucy's determination and courage, and Lucy sees that Bickslow is not just a joker but a reliable and powerful mage. This new - found understanding leads to a stronger friendship or in some cases, a romantic relationship.
In some fanfiction, Bickslow teases Lucy a lot, which is his way of showing he likes her presence. He might make fun of her in a light - hearted way about how she gets flustered around Natsu.
Often, Bickslow acts as a protector of Lucy. He uses his unique magic abilities to keep her out of danger. For example, when the guild is under attack, he positions his dolls to surround Lucy and shield her. This is because he respects her as a guild member and might have some deeper feelings for her too. He also shares his knowledge of magic with Lucy in certain stories, which helps her become a stronger mage.