BowWow has been taken to Tal Tal Heights, and once you have rescued it, you'll then need to make your way to Goponga Swamp.
If you're looking for more assistance, our Zelda: Link's Awakening walkthrough can help.
Where to rescue BowWow from Tal Tal Heights
After talking to several villagers in Mabe Village, you'll learn BowWow has been taken to Tal Tal Heights.
Though this seems like a distraction, you'll need to do this in order to reach the Gonponga Swamp and continue your quest.
This is a location that is now open to you now you've acquired Roc's Feather from the Tail Cave dungeon. Head north from Mabe Village to the Mysterious Forest, and leave via the north-east exit, where you went towards the Witch's Hut to get the Magic Powder.
As soon as you leave, you'll see a series of pits surrounding a Heart Piece. Using Roc's Feather, now only can you grab this Heart Piece, but you can then also leap north, taking you to Tal Tal Heights.
As soon as you arrive in this area, turn right, and enter the cave with the skull outside. (It's worth noting that, once you have completed the second dungeon, it's worth coming back here as just a little further right is where you unlock Chamber Dungeons.
This mini-dungeon has you face Moblin's in a series of rooms. If you forgot how to tackle them, there's a simple rule to follow no matter how they are equipped - approach with your shield raised, and after they attack and are rebuked and open to attack, attack with your sword.
The first room is simple enough - you just have to face a single Moblin - while the second pits you against four with spears. Have your shield up at all times, and only attack when you have a clear run at one of them, and repeat, lowering their numbers until they are gone.
The third and final room is against a larger Moblin mini-boss. Again, keep your shield raised - it'll be throwing a spear at you on short notice - followed by a well-telegraphed charge attack.
Move out the way and it'll bump into the wall, stunning the giant Moblin and leaving it open to attack. Repeat this until it's down. Note it can charge and stop short of the wall, but keep going and eventually it'll stun itself again, giving you a chance to inflict some damage.
Once done, you'll find BowWow in the final room. You'll now be holding onto BowWow - like taking a dog for a walk - chomping on enemies as you go.
Our Zelda: Link's Awakening walkthrough and guide can help you with the critical path, including the Eagle's Tower and Turtle Rock dungeons. There's plenty to be done on the side, too - including Zelda Link's Awakening Heart Pieces, Zelda Secret Seashells and the Zelda Link's Awakening trading sequence. Finally, there's also the new Zelda Chamber Dungeons feature to unlock and complete.
Goponga Swamp location
Lead it out of the cave and go back through the Mysterious Forest to the north-west corner, past the chest where you found the Tail Key, to arrive at Goponga Swamp.
There's not much else you can do right now outside of the swamp - there's a cave with one chest accessible for some Rupees - so press on east until you reach the swamp proper. As the sign says, it's inaccessible unless you have BowWow in tow.
Though you can hit the piranhas with your sword, it's the lilies that are indestructible unless you have BowWow on you, clearing the path to the cave at the far end.
Make sure you get the chest in the middle of the swamp as you go, too - it contains a 50 Rupee piece.
When ready, head through the cave entrance to the Bottle Grotto dungeon.
BowWow will leave your side when you enter, the by way. Don't worry - that's supposed to happen!