When using either the quarterstaff or spear as a Monk weapon, do you still gain the unarmed bonus action from Martial Arts if using 2 hands(1d8)?
On pg.78 of the PHB under Martial Arts it states that a Monk weapon cannot have the 2-handed or heavy property, so I assume since the versatile property is not the 2-handed property or heavy property then it does not matter if I use it in one or two hands. However, why then would a distinction be needed since the only simple weapon that does have the 2-handed property is a Greatclub, which is also mechanically identical to a quarterstaff used in two hands. Why make a rule that doesn't apply to anything?
The other interpretation is that you're meant to use 1d6 for damage in order to gain the Monk's Martial Arts bonus action, and using a 1d8 will forfeit the bonus because the quarterstaff is now considered 2-handed. Pg.147 under Versatile states "A damage value in parentheses (in this case 1d8) appears with the property—the damage when the weapon is used with two hands to make a melee attack."
Best Answer
The answer to your question is No, using versatile weapons with two hands does not disqualify them as monk weapons.
But not because of any reason that made you ask the question, because your whole question is wrong as it's clear from your question you haven't understood the paragraph in question.
The paragraph in question on pg. 78, PHB says (emphasis mine):
Let's look at what that paragraph really says.
The first thing it does is stating that at 1st level a monk has a master of different combat styles using unarmed strikes and monk weapons.
The second thing it does is stating that monk weapons are shortswords and any simple melee weapon that doesn't have either the heavy property or the two-handed property.
That's everything that paragraph states. It simply tells you that monks fight unarmed or with monk weapons and then defines monk weapons as either shortswords or any simple melee weapon that isn't heavy or requires two-hands to use.
Simple melee weapon with heavy or two-handed property = not monk weapons.
Simple melee weapon without heavy or two-handed property = monk weapons.
So what about the versatile property? A weapon with that property just gives you the option to use two hands during an attack for greater damage. However, in this case whether a weapon has the versatile property or not has no impact on the RAW as it only purpose in this case is to define what a monk weapon is, which is a shortsword or any simple melee weapon without either the heavy property or the two-handed property. Any other properties such as light, finesse, reach or versatile has in this case no bearing on the rules. Nor does how you use said weapon.