The Target Still Has a Reaction and Bonus Action
All creature can take an Action, Bonus Action, and Reaction each round. The Irresistible Dance spells does nothing to restrict the usage of the target’s Bonus Action or Reaction. So the target of the spell could still casts a Quickened spell using their Bonus Action or make an Attack of Opportunity as a Reaction.
The Target Must Use Their Action To Save
As you’ve pointed out, the spell includes the following line:
As an action, a dancing creature makes a Wisdom saving throw to regain control of itself. On a successful save, the spell ends.
This sentence is structured as a statement of fact (a creature makes a saving throw as an action). Many damaging spells, such as Cloud of Daggers, contain similar statements (A creature takes 4d4 slashing damage). It’s difficult argue that a creature could choose not to take the damage.
Some confusion may stem from the fact that Irresistible Dance effects a creature’s actions. Most of the other spells that effects a creatures action, such as Crown of Madness and Wrathful Smite, include the modal verbs “must”, “can”, or “may”. However, statements in 5E have their standard English meaning. The lack of a “must” from a sentence does not imply the existence of a hidden “can” or “may”.