If I were to pull a beast out of a Bag of Tricks and then cast Polymorph on it, would it be considered a willing creature or does it make a save for the spell?
It is a willing creature
From the description in the DMG, pg. 154:
You can use an action to pull the fuzzy object from the bag and throw it up to 20 feet. When the object lands, it transforms into a creature you determine by rolling a d8 and consulting the table that correspond's to the bag's color. See the Monstor Manual for the creature's statistics. The creature is friendly to you and your companions, and it acts on your turn. You can use a bonus action to command how the creature moves and what action it takes on it's next turn, or to give it general orders, such as to attack your enemies. In the absence of such orders the creature acts in a fashion appropriate to it's nature.
Since the creature is friendly, it is a willing creature for any non-harmful spells you (or your party) apply to it. Given that you control it (as per the second emboldened part of the quote above), it doesn't get to decide whether it "consents" or not (as per this answer) since it is in allegiance with you as per the magic of the Bag of Tricks.
Thus it is a friendly creature under your explicit control (well, it's controlled by the DM, but you can dictate to it and it must obey you), therefore it must be considered willing for the purposes of spells that use such wording.