I'm not trying to be a smart ass, but why do you "need to buy some [bonds] for diversification"?
Now there's diversification for diversification's sake, but ask yourself: what are you trying to achieve with your investments and specifically by adding bonds to your portfolio?
Bonds are interesting in that they are at the same time, the safest investment available and one of the riskiest investments available.
Why and why? First, and we're taking U.S. government bonds here, when you buy the bond, you are guaranteed two things: you will get your coupon payment and you will, at the end of the term of the bond, get your principle back...one way or another.
Why are they risky? Because bonds are extremely sensitive to interest rates and between the time you buy the bond and the time that the bond matures, interest rates may vary wildly and so will the price/value of your bond. If the price of your bond goes down, you don't have to sell it, but it would be rather stupid to hold a bond paying say 1% interest when you could buy one that pays 6%.
As an example, the yield on the 30 year is about 2.5%. Do you think that between now and 2046 interest rates will be such that the US30Y yield will never be (much) more than 2.5%. Doubtful. In other words, right now bonds are really only good for one thing: putting your money where it is safe and fairly liquid...since you won't be earning any interest on them (as stated, you'll actually be paying the government to hold your money for you rather than the other way around).
The important thing to remember is that bond prices are inverse to interest rates: interest rates go down, bond values go up; interest rates go up, bond values go down.
Now, with interest rates near 0% (and real interest rates negative), which way do you think interest rates are most likely to go, up or down?
So does now seem like a good time to be buying bonds?
Bottom line is if your investment horizon is 20 years (as stated) ride with equities. If sometime between now and 2036 interest rates go up to an "acceptable" level, then buy bonds.
Besides, as you get closer to living off of your investments you should gradually transfer a greater and greater % from equities to bonds* so that you are assured of having something to live off of and avoid a catastrophic drawdown.
* That is unless your stocks have done well enough that you can live off of the dividends in which case there's no need to transfer to bonds unless, as stated, interest rates are "acceptable" (i.e. significantly more than you can get from dividends).