According to the script, it's basically a gut feeling.
Thank you, Master Yoda. Do you have any idea who was behind the attack?
Our intelligence points to disgruntled spice miners, on the moons of Naboo.
I don't wish to disagree but Ithink that Count Dooku was behind it.
There is a stir of surprise.
You know, M'Lady, Count Dooku was once a Jedi. He wouldn't assassinate anyone, it is not in his character.
He is a political idealist, not a murderer.
In dark times nothing is what it appears to be, but the fact remains Senator, in grave danger you are.
PALPATINE gets up, walks to the window, and looks out at the vast city.
Count Dooku has always avoided any kind of conflict. It appears he has no desire to start a war. Why would he kill you? To what end?
I don't know, but everything in my being tells me he was behind it...
After gazing out of the window for several moments Palpatine turns to
Realistically speaking though, The Republic is in a conflict with the Trade Separatists, and she, herself, has already been a target of the Separatists. With Dooku leading the opposition who she believes is poised for war, it's not a huge stretch to believe that they may have something to do with the attempt on her life.
There have also been theories in the past, with no real hard evidence (especially in the Disney Canon) that Padme has some amount of Force sensitivity, which might provide her at least a little more insight.