There are always recurve bows, or even something smaller. A hobbit would be able to get quite close without being seen or heard so he doesn't need his bow to have as much power.
"No weapon formed against you shall prosper, and every tongue which rises against you in judgement, you shall condemn. This is the Heritage of the servants of the Lord, and their righteousness is from me." says the Lord. Isaiah 54:17
"I, the Lord, have called you in righteousness. I will take hold of your hand and will keep you and will make you to be a covenant for the people and a light for the gentiles." Isaiah 42:6