The increase in the money supply halves, not the money supply itself.

More importantly, your assertion that value of a bitcoin is more volatile because of the fixed money supply is flawed. The flaw is the conflation of "supply" in "supply and demand" and "money supply". The meanings of the word "supply" in these two concepts are very different. The quantities of bitcoins available to meet demand (the "supply") comes from holders of bitcoins. You cannot claim that supply is fixed just because the money supply is fixed.

As the quantity in the supply curve approaches the money supply limit, we can assume that the price and slope approach infinity, and near that point the supply is inelastic and the price is very volatile as you claim. However, note that increased hoarding of bitcoins (or simply holding) raises the supply curve and moves the intersection with the demand curve away from the money supply limit and towards higher elasticity and decreased volatility.