In The Hobbit, does Bilbo decide to go on the adventure because he doesn't like being described as cowardly or is it because of his Tookish instincts?
No one could call Bilbo Baggins cowardly. In The Hobbit, Bilbo plainly tell Gandalf he has no plans for an adventure. However, his mind is slowly swayed when a virtual fleet of dwarves show up and enter his hobbit hole. They stay for meals and sing their songs. The dwarves' final song talks about the odyssey they will begin in the morning. They will travel over the misty mountains, enter the dragon's lair, and reclaim their harps and gold.
"As they sang the hobbit felt the love of beautiful things made by hands and by cunning and by magic moving through him, a fierce and jealous love, the desire of the hearts of dwarves. Then something Tookish woke up inside him, and he wished to go and see the great mountains, and hear the pine-trees and the waterfalls, and explore the caves, and wear a sword instead of a walking-stick."
Although Bilbo immediately has a change of heart, ultimately his Took heritage overpowered him and he could not reject adventure.