A bound form is a °form that cannot occur on its own as a complete utterance.
The term bound form has been defined in a rather consistent way since Bloomfield, as opposed to free form. However, this definition is not widely known among linguists, and in practice, "bound" is often equated with "(orthographically/phonologically) attached to a root/stem". But "attachment" is not well-defined (see https://dlc.hypotheses.org/2847), so it is better to use bound and free in the original Bloomfieldian sense. Clitics are not normally thought of as "attached", but they are bound forms in that they cannot occur on their own (Haspelmath 2023).
“A linguistic form which is never spoken alone is a bound form; all others ... are free forms.” (Bloomfield 1933: 160)
“Forms which never occur alone as whole utterances (in some normal situation) are bound forms; forms which may occur alone as utterances are free forms.” (Lyons 1968: 201)
"bound form = A morpheme that may not stand on its own and must be attached to a stem." (Aronoff & Fudeman 2011: 260)