It might not be as simple as hoping on a bus but it is as simple as hopping on a train!
RER Line C runs direct to Versailles-Rive Gauche station. The southern part of Line C basically follows the Left Bank of the Seine (i.e. the southern side of it), serving such stations as Champ de Mars-Tour Eiffel (for the Eiffel Tower), Museé d'Orsay (for the museum) and St Michel Notre-Dame (for the cathedral and the Latin Quarter), so it's easy to fit in the Château de Versaiiles with many other tourist attractions.
A Passe Illimité ticket, covering the whole of the Paris Transportation area (including Line C all the way to Versailles-Rive Gauche station) costs €22.20 for one day, €33.70 for 2 days, €47.25 for 3 days or €57.75 for 5 days. It gives unlimited travel on buses, trams, Metro services and RER trains.
However your friend probably would only the need a 'whole city' pass for just the one day (to visit Versaille). On any other days she could use a 2-zone Passe Illimité ticket, which covers all of the central tourist attractions. A 1 day ticket costs €10.55, 2 days costs €17.15, 3 days costs €23.40 and 5 days costs €33.70.
Paris is one of the easiest cities in the world to find your way around. Using the RER trains (which are like a 'limited stop' version of the Metro) is usually the quickest way to travel.
Chris