From the manual:
trap [-lp] [arg] [sigspec …]
The commands in arg are to be read and executed when the shell receives signal sigspec.
The description doesn't say anything about adding to an existing list of commands. It goes on to specify non-incremental effects when arg is empty or the string
-. While the text might not explicitly say that the commands are not added to a list, it never mentions any such list, or any means to remove an item from said list. So interpreting this text in a way that would imply that successive
trap commands add
arg to a list is rather far-fetched.
You can make sure by checking another shell's manual. If bash deviated from the usual behavior, the manual would clearly say so. The POSIX standard is unambiguous on the matter:
The action of trap shall override a previous action (either default action or one explicitly set).