In Advanced Styler, under this

css
/* Styling for the chat bubble content when it's from the user */
.bpw-from-user .bpw-chat-bubble .bpw-chat-bubble-content {
  background-color: #6675fa;
  color: #ffffff;
}

add this with the hover effects you need

css
.bpw-from-user:hover .bpw-chat-bubble:hover .bpw-chat-bubble-content:hover {
  color: black;
}

Add ":hover" after the element you want to change, and then the change you want to make, here text changes to black.