I think that your grammar and syntax are right.
Especially your first line, Ecclesia semper reformanda. This is a classic motto, and it means exactly what you say.
Your second line, Spiritus Sancti ductu et auctoritate Bibliorum is fine as well. Auctoritas is obviously cognate with "authority", but in Latin I think it maybe means something more like the personal influence of one person on another. You might be able to find another word that is, arguably, a better fit for the authority of the Bible.
A couple of alternatives, depending on your aims:
Matthew 7:29 uses uses potestas as in Erat enim docens eos sicut potestatem habens, et non sicut scribae for "he taught them with authority, and not like the scribes".
You could object to the vagueness of potestas, which can mean any kind of power or capability, and not just "authority". Such vagueness could be a feature in certain contexts, and a bug in others. A Latin word meaning "teaching authority" is magisterium, and it might make a good fit for your purposes.
The usual word for legal authority is imperium. I'm not sure that's exactly what you're trying to say here, though.
If you decide to go with potestas, magisterium, or imperium, be sure to put them in the ablative like you've already done with auctoritate: potestate, or magisterio, or imperio.