The personality traits, or character traits, of a character are all part of an author's characterization. We can analyze characterization and learn about personality traits by looking at things the character says and does. We can also learn about personality traits through analyzing other characters' responses to the character in question.
One thing we know about Bottom is that he thinks very highly of himself; we can even call him arrogant. What's more, he has very little reason to think so highly of himself; hence, his foolish arrogance is a key reason why Puck decides to give him a donkey's head. The donkey's head represents Bottom's stubborn, foolish, and arrogant personality. We especially see Bottom's arrogant personality when he keeps demanding that he be allowed to play the other actor's roles, showing us that he thinks very highly of his own skills and very poorly of anyone else's. His ideas for the play are not only arrogant, they are also foolish because it is very unrealistic for him to play more than the lead male role. We see this when he requests to play Flute's role of Thisbe as well as his own role as Pyramus, saying that if he hides his face in a mask, he can play both parts, as we see in the lines, "An I hide my face, let me play Thisbe too. I'll speak in a monstrous little voice" (I.ii.46-47). He even asks to play the lion as well (65).
Not only do we see that Bottom is arrogant and thinks too highly of himself, we also see that he has a very bossy nature. We particularly see this in the way that he bosses Quince around, especially giving him commands about how to conduct his business, as we see in the lines, "You were best to call them generally, man by man, according to the scrip" (2-3). Bottom even proclaims his own bossiness by referring to himself as a tyrant in his line, "[Y]et my chief humor is for a tyrant," meaning that he mostly aims at being a tyrant, or playing a tyrant. We even see Quince confirm Bottom's bossiness in the pun he uses to address him in the line, "What sayest thou, bully Bottom?" (III.i.7). While in Shakespeare's era bully was used to refer to a good friend, it also refers to a "quarrelsome, overbearing person" (Random House Dictionary).
Hence, a few things we know about Bottom's personality traits is that he is arrogant, thinks too highly of himself, is foolish, stubborn, and is very bossy.