How can the bond market be overvalued when the value of a bond is a function of interest rates?
How can the bond market be overvalued?

To value a bond, you need, as you mention, to discount future cash flows. The cash flows (or coupons) are fixed, but the discount rate is not, and every investor may have a different view on interest rates and hence price bonds differently. 

Therefore, someone thinking that interest rates will remain at rock-bottom levels will find different prices for bonds from someone who thinks that interest rates will rise sharply in the near future (the first investor will find higher prices).

So, in your case, someone thinking that the bond market is overvalued simply has a different view on interest rates than the consensus on the market. To be more precise, they expect interest rates to increase faster than the market consensus.

Bond Prices and interest rates 

Taking into account what we have said above, you can view the bond market as follows: every investor forms a view on discount rates, for a given bond. Doing so, they actually compute the yield, that is the discount rate that makes the NPV of the cash flows of the bond equal to 0.

However, investors disagree on where the yield should be. They will thus trade the bond between them until they all agree. 

Let's take a numerical example :


Investor A owns a Bond, which has a face value of 100, a coupon of 1 and will mature in one year.
Investor A thinks that the yield of this bond should be 2%
Investor B thinks that the yield of this bond should be 0.5%


The value of this Bond to Investor A is : $(100 + 1) / 1.02 = 99.02$
The value of this Bond to Investor B is : $(100 + 1) / 1.005 = 100.50$

Therefore investor A and Investor B will both improve their current state by trading the bond anywhere between \$99 and \$100.5, ie. Investor A should sell the Bond to Investor B.

If the market price of the bond is \$100, then Investor A thinks that the bond is overvalued, and Investor B thinks that the bond is undervalued.