Sidious and the Senate?

Sidious waited nearly 20 years to properly dissolve the senate after becoming Emperor. Why did he wait so long?

Because he was the Senate

Right. So why even keep it active for all those years?

Because it served as a transitional buffer between the Old and New, it just outlived its usefulness by the time, that and those who were against Palps were in the Senate.

The Senate was just a facade, tbh. Truth is, Palpatine (and Tarkin) were fully calling the shots, and could bypass the Senate whenever they felt like it.

Palpatine kept the Senate 'intact' to give the galaxy at large the perception that democracy was still a thing -- it helped prevent a greater uprising from the people. But once the Death Star was complete, and Palpatine could rule the galaxy with an iron fist solely through fear, he dissolved the Senate immediately.

So in answer to your question: the reason it took Palpatine so long to get rid of the Senate is because he was waiting for the Death Star to be built.