If you're using a monk weapon, you should be able to use the Bonus Action unarmed strike (and flurry of blows) even if you're wielding a shield in the other hand.
Martial Arts
At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
You gain the following benefits
while you are unarmed or wielding only monk weapons and you aren't wearing armor or wielding a shield:
You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels, as shown in the Martial Arts column of the Monk table.
When you use the Attack action with an unarmed strike or a monk weapon on your turn,
you can make one unarmed strike as a bonus action. Flurry of Blows is allowed but no BA unarmed strike.
