Am new to bonds. How important is it to diversify bonds across both international and US firms as compared to diversification within the stock portfolio?

Am a young investor so to this point have been fine with a 100% stock portfolio with market weighted international vs. US balance. However, I am starting to look at adding bonds to my portfolio and don't seem to have an option for an investment grade international bond index as part of my investment options, just US bonds. How much performance gap is there between US vs. international bonds? How much does overperformance of US/international bonds correlate with overperformance of US/international stock indices?