I agree with the previous answer in terms of the transitive verb. But there is another piece to the analysis of parallelism in this example—and why the correct answer is been caught and not have been caught. (Despite what you stated, it's not actually wrong because of subject-verb agreement.)
The sentence could be written as:
On my bike, I have enjoyed the beautiful weather, have endured freezing cold, and have been caught in sudden cloudbursts.
All three items now use have, so this is a good example of parallelism.
By contrast, it could be written in the form of a vertical list.
On my bike, I have:
* enjoyed the beautiful weather,
* endured freezing cold, and
* been caught in sudden cloudbursts.
Here, none of the items use have, so this, too, is a good example of parallelism.
You might look at the version that's marked as correct and wonder why the first item uses have while the other items don't. But you can consider it as if the have that's there belongs not to the first item but to the set of all items. Or you can think of it as a form of elliptical construction, where it's omitted from the other items but its presence is still implied.