First, while gerere can mean "to bear, carry", it also can simply mean "to do*, as in the res gestae, not "things carried," but "things done." This stems from a meaning close to English usage, where we have "to carry" and "to carry out," where the latter simply means "to do."
The name was chosen to connote the usage of gerunds and gerundives. Since gerunds come directly from the verb, the name gerund is used to describe how they are conceptualized. Let's take loqui as our example. To get from loqui to loquendum, someone would have to perform an act of loqui. In other words, they would have to carry out (= do) the act of speaking.
Gerundives too originate similarly, but passively and in the future. Verba loquenda are not "carried words," but rather "words to be carried out," which is equal to "words to be spoken." This is also where the necessity in gerundives come from. Things that are to be done in the future yet are currently not done must be done. See CerberusCerberus' post on that for more information.