Hey! I need some help with my Ranger! I made it to level 2 and chose Two-Weapon Fighting as my fighting style. I understand that I keeps bonuses for her offhanded weapon. However, as I understand there rules for 5e, a character can attack with an offhand weapon as a bonus action, and I'm just not finding where a Ranger gets that bonus action.

What am I misunderstanding? Help!

dual wielding is something every people can do. so its basically from the basic rules.
but your bonus action adds your off hand damage bonus, which others don't.

Bonus actions are not granted by class or races, they are granted by the action itself. So, you take Two Weapon Fighting and it grants its specific bonus action. You take the Pole Arm Master feat and it grants a specific bonus action. You become a monk and you get certain specific bonus actions. You select the spell hunter’s mark and it grants you the bonus action in which you caste it, etc. However, you are only allowed to take 1 bonus action each round IF you have bonus action actions.

Chapter 9 of the players handbook provides the information you are requesting. A simple synopsis is that on your turn you can move and take an action. If your character meets criteria to take a bonus action then you may do so. The action can spell, interaction, additional movement, ability to enhance an attack, etc.; and the rules for this particular action will define it as a Bonus Action (or BA). Any character can take only one bonus action on their turn and that action must be defined as a bonus action. It is not guaranteed that a character can take a bonus action. 

Further in this chapter, the bonus action of a second attack is defined. Again, this applies to all classes and races of characters provided they meet the criteria to take this bonus action which are: 

1) The character is wielding a one handed weapon with the light property in each hand
2) The character takes the Attack action. They may use their bonus action to make a second attack with the other weapon (with the light property)
3) The second attack does apply the ability modifier to the damage (unless if the the modifier is negative). 

The feature you took for your character would negate item 3) and allow you to add a positive ability modifier to your damage. 

To mirror comments form other posters, what you need to identify class features or spells you have access to that use your bonus action. If you use your bonus action for one of these examples then you cannot take the second attack on that turn. 

Others have granted relevant information, though I'd like to provide an alternate phrasing of the rules for bonus actions.

Some features grant you a bonus action. You can only take 1 bonus action during your turn, and you only have a bonus action if a feature grants one. A bonus action is simply an additional action you can take to activate the relevant ability (for instance, two weapon fighting).

Equip two weapons. Click on one, click customise and check "Dual Wield". That one will now move to show under "Bonus Actions".