What's the point of that? Why not vote on the drafted bill?

Because the budget and reconciliation processes are more complicated than that, and the bill hasn't been drafted yet.

In a nutshell, the chambers first vote on a series of budget resolutions that establish some top-line numbers and include directions to the various committees in how to draft the portions of the spending packages that fall within their jurisdiction. Here's a primer on the process and the Senate bill:

A budget resolution is a document that outlines desired spending, revenue, debt, and deficit levels for the federal government over a specified period (often 10 years). It is the first step Congress is supposed to take in order to pass annual spending bills ahead of the October 1 start of the fiscal year; it also enables the reconciliation process. Under the 1974 Congressional Budget and Impoundment Control Act (CBA), Congress is supposed to complete action on the budget resolution by April 15, though it often fails to do so.

bipartisanpolicy.org - Whats in the senate budget resolution

The hardline fiscal conservatives in the House were upset because the Senate budget resolution included relatively modest instructions to reduce spending, compared to the House. The Senate bill only directed $4 billion in spending cuts, compared to the more than 1$ trillion in the House reconciliation instructions.

Now the work of actually drafting the BBB begins. Because the instructions represent a floor on spending cuts, the House holdouts were mollified by public assurances by Thune (and presumably others) that the Senate will actually end up cutting far more than the reconciliation instructions mandate as a minimum.