This is a good question, presently there is a huge gap in Canon between Episode I and Episode II. It looks like not only Jedi were busy doing nothing, but Palpatine wasted almost two of his terms. Quote from novel Tarkin :
“The Supreme Chancellor is not required to bribe me into remaining
loyal to him.”
“As a complement to previous bribes, you mean. In allowing your
illegal actions in the Seswenna to go completely unchecked since you
abetted in the undermining of Finis Valorum.” Dooku snorted in scorn.
“A strong leader would never have allowed galactic events to reach a
point of crisis. He is weak and inadequate.”
Tarkin shook his head negatively. “He is hemmed in by a corrupt and
incompetent Senate. Otherwise the Republic would have already raised a
military to oppose you.”
“Ah, but the end of his second term is upon him, Governor, with no one
of any merit to succeed him. Unless, of course … some crisis results
in his term being extended.”
Of course, something was happening behind the scenes, but there were no apparent results. Jedi were none the wiser at the beginning of Episode 2, then they were at the end of Episode 1. They even didn't suspect Dooku who left the Order. We could only hope that Disney or who ever owns SW franchise would find interest to cover Anakin's Padawan years with Obi-Wan, so we could get some information what happened in that period .