If the US Senate Majority Leader doesn't want to bring a bill to the floor for a vote, are there other mechanisms that would allow the bill to be voted on anyway? If so, what are they?
Yes. There are two main ways that this can happen. As explained at the U.S. Senate website:
Senate rules also permit a measure to be placed directly on the calendar when introduced or received from the House. This process permits senators to bypass referral to a committee they believe unsympathetic. Alternatively, if a committee fails to report a measure, a new measure with exactly the same provisions may be introduced and placed directly on the calendar.
Finally, Senate rules do not require that amendments be germane or relevant, except to general appropriation bills, budget measures, and matters under cloture (and a few other bills, pursuant to statutes). Consequently, if a committee fails to report a measure, a senator may offer its text as an amendment to any other measure under consideration, without regard to the scheduling preferences of the majority leader.
Motions To Discharge
When Senators force a matter to be considered by the Senate as a whole, rather than subject to the default rule that causes all new matters to automatically be referred to the committee or committees designated by the Majority leader, whose chairs can defer consideration of the bill indefinitely, this is called a Motion to Discharge. These motions are discussed in the Senate Rules, in a manner that is hard to understand unless you already know what they mean, here, which, in turn, has to be understood in the context of a couple of other rules that influence how this plays out that provides context for these Motions in the larger scheme of U.S. Senate procedure.
As a practical matter, however, this doesn't completely deny the Majority Leader a say over the question entirely, because the Majority Leader has some discretion over when the Senate will consider a Motion to Discharge.
So, a Motion to Discharge is more often used when the Majority Leader wants to override a non-compliant committee chair whose committee has had a bill referred to it for consideration upon introduction in the Senate, than it is to circumvent the Majority Leader's power to schedule when matters will be considered by the Senate.
More frequently, a Senator forces consideration of a matter over the objection of the Majority leader by making a non-germane amendment (i.e. an amendment to pending legislation which is unrelated to the substance of what is being considered) to any bill being considered on the floor of the Senate.
When a bill is already being considered by the Senate, any Senator has the right (subject to exceptions noted above) to propose an amendment on any subject matter to the bill pending under the Senate's rules, unlike the U.S. House whose rules allow amendments to bills it is considering only to the extent that the "Rule" of the Rules Committee governing how a bill will be considered on the floor of the U.S. House permits an amendment to be considered. As explained in the non-germane amendment link:
An even more important opportunity for individual Senators is a result of the absence in the standing rules of any general requirement that the amendments offered by Senators on the floor must be germane or relevant to the bill being considered. The rules impose a germaneness requirement only on amendments to general appropriations and budget measures and to matters being considered under cloture; various statutes impose such a requirement on a limited number of other bills. (The Senate generally interprets germaneness strictly, to preclude amendments that expand the scope of a bill or introduce a specific additional topic.) In all other cases, Senators may propose whatever amendments they choose on whatever subjects to whatever bill the Senate is considering.
The right to offer non-germane amendments is extraordinarily important because it permits Senators to present issues to the Senate for debate and decision, without regard to the judgments of the Senate’s committees or the scheduling decisions and preferences of its majority leader.
Again consider the position of a Senator whose bill is not being acted on by the committee to which it was referred. Instead of introducing an identical bill and having it placed directly on the calendar, he or she may have a second and typically more attractive option: to offer the text of the bill as a floor amendment to another bill that has reached the floor and that can serve as a useful legislative “vehicle.”
The possibility of this opportunity can make it extremely difficult to anticipate what will happen to a bill when it reaches the floor and how much of the Senate’s time it will consume. The party leaders and the bill’s floor managers (typically, the chair and ranking minority Member of the committee with jurisdiction over the bill) may know what amendments on the subject of the bill are likely to be offered, but they cannot be certain that Senators will not want to also offer nongermane (and often quite controversial) amendments. In fact, it is not unusual for one or more non-germane amendments to occupy more of the Senate’s attention than the subject the bill itself addresses.