No not really, a carriage or coach bolt more properly called a cup square square in its galvanised form is the correct bolt for this application as not only is it rust resistant but also has the correct tensile strength for the job. Whilst you could use roofing bolts they are not as strong and could fail mechanically(shear). High tensile galv bolts will in all likelyhood be dearer and you wont have a nice smooth head with no edges to catch clothing.

Yes there are cheaper bolts to use but they will rust.

Nope. Galvanized are going to be the least expensive in the *rust resistant* category. They will rust eventually, but anything else will either rust much quicker, or not at all. The *not at all* ones (brass, stainless steel etc.) are going to cost a lot more. Stick with the galvanized if cost is that important.Personally, if it's exposed to weather, I'd rather spend the extra for stainless.
Al