Solar Cave
The first dungeon you'll need to conquer for obtaining the Friend Bow is Solar Cave. Unlock it by going to Town Square and speaking with Medicham, Lombre and Whishcash. Bring a water Pokemon along with you to obtain the Surf move from the 20th floor. You'll need to have this move to gain access to the upcoming dungeons. Before completing Solar Cave, make sure you've acquired an extra key; you'll need it to find the Friend Bow.
Mt. Faraway
After you've made it through Solar Cave, you'll find a Spinda in Pokemon Square who will give you a Clear Feather. Take it to Xatu in the Great Canyon area to open the next set of dungeons. Make your way through the Fiery Field, Lightning Field and Northwind Field dungeons to gain access to Mt. Faraway. Search the 30th floor of Mt. Faraway to find a locked door. Open the door with your key to find a Friend Bow.
Joyous Tower
It's the less reliable method of obtaining a Friend Bow, but you can also try taking your chances in Joyous Tower. Unlock this dungeon by recruiting Latios and Latias from Northern Range and Pitfall Valley. You will also need the Sky Blue Plains Friend Area. Once you've gained access to Joyous Tower, check the Kecleon shops in the dungeon. Sometimes these shops will offer the Friend Bow for purchase.
Utilizing the Friend Bow
With the Friend Bow in your inventory, you can finally begin to reap its benefits. Equip the Friend Bow to your team leader when you're attempting to recruit a Pokemon. Have your leader deliver the final blow during the fight to enable the bow's recruitment influence. To further boost your recruiting abilities, raise your team leader's level as high as possible. The maximum recruiting boost possible in the game is 24 percent, at level 90 and above. The boost increases to 34 percent with the Friend Bow equipped.