Were His disciples and believers in Him just supposed to live their lives according to what the Bible said about Him?
Yeah. For example, some of the things the Bible said about Him were the truths that He is God, and that He was crucified, died, was buried, rose from the dead, and ascended to heaven. To live according to those truths is to live according to what the Bible said about Him.
How was that supposed to work, when there was no New Testament when He ascended?
What do you mean by
"there was no New Testament when He ascended"? Do you mean that those
Bible Truths (that He is God, and that He was crucified, died, was buried, rose from the dead, and ascended to heaven, etc.) weren't believed by
"His disciples and believers in Him" until the New Testament was penned? Do you mean that those
Bible Truths (that He is God, and that He was crucified, died, was buried, rose from the dead, and ascended to heaven, etc.) weren't true until the New Testament was penned? Was
the Bible Truth that Jesus is God somehow
not true until it was written in the New Testament that Jesus is God? Was
the Bible Truth that Jesus raised Himself from the dead somehow
not true until the New Testament was penned? The penning of the New Testament didn't cause any of those Bible Truths to be true.