Is it possible to make bullets using a regular script, not a local script?

You'll need to have your bullet inside of ReplicatedStorage. Make sure it's one singular model/mesh, that way it's easier to script, and you don't have to get the hard parts of moving a model. Next, you'll need to type this script:

local player = game.Players.LocalPlayer
local mouse = player:GetMouse()
local part = game.ReplicatedStorage:WaitForChild("bulletname")
local startPoint = part.CFrame.p -- This will be the firing point basically
local speed = 100

mouse.Button1Down:connect(function()
local lookPoint = mouse.Hit.p
local projectile = Instance.new("Part") -- Creating the projectile (I'm pretty sure you know how to edit it by using Instance.new with a mesh and configuring it.)
    projectile.Parent = workspace
            projectile.CFrame = CFrame.new(startPoint,lookPoint) -- Projectile starts at "startPoint", while looking at "lookPoint"
            mouse.TargetFilter = projectile -- The mouse will ignore the projectile so it doesn't end up above the mouse position   

local BV = Instance.new("BodyVelocity") -- Creating body velocity
    BV.Parent = projectile -- parenting it to the projectile
        BV.MaxForce = Vector3.new(math.huge,math.huge,math.huge) -- Setting max speed
    BV.Velocity = projectile.CFrame.lookVector * speed -- It will fly in the direction the projectile is facing multiplied by the Speed
end)