Do I need an LLC AND liability insurance?

1) You would not be liable for what the user does with the bow. You could be liable if the bow is defective (e.g. you do not properly laminate any wood used in its construction, or the bow limb geometry is wrong, putting too much strain on the bow, or you use flawed materials, etc.) and it snaps mid-draw or otherwise breaks and injures a person. That is, you may be liable for what you do in design and construction, but not for what someone else does with your product.
2) Therefore, yes--you should have liability insurance.
3) You should have an LLC. 
a) Having an LLC insulates your personal assets (e.g. house, car, money in the bank) from most business-related debts or liability (it's not 100% protection, but it is very good protection). Thus, if there was a product liability suit and it exceeded your insurance, you would still be personally protected from it--only the business, not you, would have to pay.
b) Under the new tax law, it appears that "pass through" entities like LLCs get some favorable tax treatment (possibly a 20% deduction). Also, having a separate LLC (and keeping it funds, costs, etc. fully separate from yours) will facilitate deducting business expenses.
c) The LLC-fees are themselves tax deductible business expenses, reducing their effective costs.