US Constitution Article 1 Section 5 Clause 2: Rules
Each House may determine the Rules of its Proceedings,...
This includes how discussions are held and how votes are brought to the floor.
President of the Senate
Unlike in the House of Representatives, where the Speaker is both the presiding officer and the leader of the majority party, the presiding officer in the Senate (whether the Vice President of the US, the President Pro Tempore or a junior senator who is just filling in) has little political power according to Senate rules. The main powers are to cast tie-breaking votes and to make judgments about parliamentary rules (which can be appealed to the whole chamber - incidentally, this is how the "nuclear option" was invoked). Otherwise, the majority leader, committee chairs and even individual senators share the power, and the presiding officer must mostly act as they wish. If that means the majority leader (backed by the majority party) do not want to hold a vote, then the presiding officer must respect that under the rules.
Even if the presiding officer was particularly brazen and did not respect the rules, the senators in the majority could begin a quick rebellion using tactics like e.g. fleeing to eliminate a quorum (see below). At some point, the executive branch needs the Senate to accomplish its goals (e.g. passing appropriations), and so fomenting a rebellion among senators would be counterproductive.
Why can't the rules change? The Senate is a permanent body since only 1/3 of senators' terms expire at the end of a given Congress, unlike the House of Representatives, where all members' terms expire at the end of every Congress. Since the Senate is permanent, its rules live on between Congresses. Rule changes require either a supermajority or the politically-fraught "nuclear option."
The Presiding Officer may at any time lay, and it shall be in order at any time for a Senator to move to lay, before the Senate, any bill or other matter sent to the Senate by the President or the House of Representatives for appropriate action allowed under the rules and any question pending at that time shall be suspended for this purpose. Any motion so made shall be determined without debate.
This rule allows the presiding officer to supersede pending business with two major constraints: the superseding matter must be from either the President or the House or Representatives and whatever action must be an "appropriate action allowed under the rules." This rule is used for things like announcing that the president has made a nomination, that the president has vetoed a Senate bill or that the House has passed a bill, all three of which require action by the Senate. Other rules (both precedents and explicit rules in the Standing Rules) govern what the appropriate actions are (in general, a first reading and then referral to committee).
The Constitution requires that each house can only conduct business when a quorum is present, and defines as quorum as a majority of members of each respective house. This means that if a minority party (or a presiding officer aligned with them) attempted to take command, the majority party could simply flee en masse, leaving only one member to raise points of order about the absence of a quorum and so on. The Senate rules allow a minority of the Senate to empower the Sergeant-at-Arms to arrest vacant members and bring them back to the Senate, but it would still be very hard to do this on a mass scale. (Something similar happened several years ago in Wisconsin, where a slim Republican majority in the state legislature were trying to pass legislation that would weaken unions, and Democrats in the state senate fled Wisconsin. Wisconsin requires a quorum of 60% of members, so in that case the minority party had an effective veto.)