Long term bonds have not always been negatively correlated with stocks, that has been a trend that started during the dotcom bubble. Historically it has varied and you should expect the correlation will become positive for some decade within your lifetime. Bond yields historically low right now, which may indicate more risk or less return.
Which isn't necessarily a recommendation against. I keep 5% in long term treasury bonds, but would recommend not more than 10-20% at most. VLGSX is a nice low cost option if you prefer a mutual fund. Otherwise I suggest GOVZ (if it keeps its low fee), ZROZ, or EDV. These are extremely long term bond funds because they own bonds which have been stripped of their interest payments, but it means you can get a similar size effect in terms of price movement while risking a smaller portion of your money.
There are lots of other options which I would recommend at least as highly, since you are currently S&P500 only. For example S&P600 value, such as SLYV. International funds are a big part of the investable universe. Other bonds, such as Series I saving bonds. Generally I would recommend the S&P500 be not more than 40% of the investments of someone in your position (50% if VTI). My recommendation:
50-90% stocks
Not more than 50% total US stocks
International 20-50% of stock allocation
Not more than 40% bonds
A real asset, eg real estate, is nice.