The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, κ(φ)=200 to 300k(B)T. For DNAs of lengths N=40 to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100μs are found. The bubble starts winding from both ends until it reaches a ≈10 bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on κ(φ) and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.