One common theme is the struggle with identity. Bilbo as a vampire has to come to terms with his new self. Another is the isolation that often comes with being a vampire in a world that doesn't understand them. And of course, there's the theme of forbidden love, as his vampiric nature might put barriers in his relationships.
The theme of survival is quite common. Bilbo has to find ways to survive as a vampire, whether it's finding suitable sources of 'food' or dealing with those who would hunt him. Also, the theme of redemption can be found. He may have done things as a vampire that he regrets and tries to make up for, adding a moral dimension to the story.
A major theme in these fanfictions is the relationship changes. His friends, like the dwarves or Gandalf, might react differently to him as a vampire. Also, the theme of temptation is present. The urge to drink blood and how Bilbo resists or succumbs to it is often explored in detail. For example, in some stories, he has to find alternative ways to satisfy his vampiric thirst without harming the innocent. This adds a layer of complexity to his character and the story as a whole.
The theme of redemption can also be found in some 'dragon bilbo fanfiction'. Maybe the dragon has done bad things in the past and through its relationship with Bilbo, it tries to redeem itself. And of course, the theme of magic is prevalent. Dragons are magical creatures, and when combined with Bilbo's world, it creates a lot of magical elements in the stories.
Adventure is a very common theme. Since Bilbo is known for his adventures in Middle - earth, fanfictions often involve the reader joining him on these exciting quests. Another common theme is friendship. The relationship between the reader and Bilbo grows as they face challenges together.
One common theme is empowerment. Female Bilbo is often shown as a strong, independent character who can hold her own in a male - dominated world like Middle - earth. For example, she might be the one to come up with clever solutions to problems that the dwarves can't figure out.
One common theme is self - discovery. Young Bilbo is often portrayed as trying to figure out who he is and what he wants in life. For example, in many fanfictions, he starts to question the simple, comfortable life in the Shire and yearns for something more adventurous.
Love is also a prevalent theme. Whether it's a platonic love or a romantic one, many fanfictions play with the idea of their feelings for each other. Some explore how their different backgrounds, Thorin as a dwarf king and Bilbo as a hobbit, influence the way they express their love and care for one another. It can be a very interesting exploration of their characters' emotions.
Redemption can also be a theme. Thorin's pride and how he might overcome it with Bilbo's help is something seen in some fanfictions. And loyalty, both to each other and to the company they are part of, is frequently a central theme as well. For example, in some stories, they are tested in terms of their loyalty to one another during difficult situations.
A common theme is the influence of Bilbo on Frodo. Since Bilbo has had so many adventures, he passes on his wisdom and stories to baby Frodo.
One common theme is the exploration of different cultures. Thranduil is an elf king and Bilbo is a hobbit, so their cultural differences play a big role. Another theme is the idea of finding love in unexpected places. Their relationship is not something that one would expect in the original Tolkien lore.
One common theme is the aftermath of his adventures. For example, dealing with the trauma of facing the dragon Smaug or the battles in Middle - earth.