According to this guide, there are only 5.
As soon as you have your Sword and Shield in hand, head on over to the Bazaar in the middle of Skyloft and speak with Luv, the owner of the Potion Shop, and she will inform you about her potions. After noticing that you don’t have one, she will provide you with an Empty Bottle that she was storing.
When you enter the temple at the Sealed Grounds for the first time, before speaking with the old woman at the top of the stairs, look over to the right of the stairs. Here you will find a small brown chest, and inside will be your second Bottle, prefilled with Revitalizing Potion.
Bottle #3 can be obtained by completing the Missing Sister side quest, which becomes available after completing the Lost Child side quest. (The Lost Child quest should be completed ASAP as it unlocks the ability to perform additional side quests that yield great rewards that will be extremely helpful throughout the rest of the game.
Once you obtain the Mogma Mitts in the Fire Sanctuary, Head back to the first floor. Locate the circular room in which you can now dig underground. Take Link underground and hit the switch to open the gate above you; this will open a new path filled with water plants. Use the switch nearby in order to open more gates and poke one of the water plants to skewer it with your sword. Head through the gate and make a right. Kill the Magmanos (slash to toss the water plant at it, then slash the Magmanos itself); this will lower the lava level giving you access to a new path which ends with a chest containing your fourth Empty Bottle.
This bottle is located inside a Goddess Cube Chest that becomes available after striking a Goddess Cube in the Eldin Volcano. This cube cannot be reached or seen until the second trip to this location.