You are correct. Read the base save of a Barbarian 3, base save of a Bard 6, and add them.
Factional BAB & Saves: Variant Suggestion
I strongly recommend, however, that you use the “fractional” variant. In 3.5 that’s in Unearthed Arcana; I don’t know if Pathfinder replicated it anywhere, but saves work the same way in both so the variant works fine in Pathfinder.
The idea is that good saves are 2+½level and bad saves are ⅓level (you can confirm this by looking at a few classes’ save progressions). Full BAB (Barbarian, Fighter, Ranger) is equal to level, medium (Bard, Cleric, Rogue) to ¾level, and poor (Sorcerer, Wizard) ½level. Under fractional BAB/saves, you add the BAB/saves of your different classes together before you round down.
The reason for doing this is because if you take 3 classes that have the same bad save, under the usual scheme you have a +0 (0+0+0) but with fractional you have +1 (⅓+⅓+⅓). As you continue to multiclass, this problem gets worse and results in wonky saves that are arbitrarily lower than they should be even for a bad save at your level. Using the fractional system just keeps the numbers more consistent so you cannot accidentally screw yourself.
Repeated +2: Another Houserule Suggestion
Good saves, as mentioned, are 2+½level. Thus, every time you multiclass into a class that has a particular save as good, you get another +2. Just like multiclassing multiple classes with the same bad save under the normal scheme can result in inappropriately-low saves, multiclassing several classes that have the same good save can result in inappropriately-high saves.
The solution to this is simple: houserule that you can only get the +2 to a good save the first time you get it as a good save. (This is how the variant is presented in a later "save my game" article.)
Including Prestige Classes
For Prestige classes, the save progression is also either good or bad, but in Pathfinder for whatever reason the progression has been shifted (and good saves lose the +2). Under the fractional system, these changes don’t make sense and should be ignored (even under the default system, they make limited sense). Just note if a save is good or poor, and treat the prestige class levels as levels of good or poor save progressions, as normal. Note that “good” saves start at +0 while “poor” saves start at +1, because this shifting was poorly-considered and shifts good and poor saves differently.
I typically strongly suggest both fractional and no-repeated-+2 for games I play in. They result in everyone having base saves that are roughly “level appropriate” regardless of the timing of any multiclassing.
It’s worth noting that you do not actually have to keep track of or add fractions to use the fractional system: you can just say “I have a total of 5 levels that have this save as bad and 3 that have it as good; that’s 5×⅓ = 1⅔ for the bad saves and 3×½ = 1½ for the good saves.” Add them together and then round down (as normal for fractions in d20) to get +3, add +2 because you do have at least one level with a good save. The system doesn’t care if you had poor-save-class 5/good-save-class 3 or poor-save-class 1/good-save-class 1/poor-save-class 1/good-save-class 2/poor-save-class 3: with both of these variants, you get the same base save bonus.