I'm assuming you are buying bond mutual funds or bond etfs here, not the actual bonds directly.
There are a significant variety of different types of bond funds, reflecting the sort of bonds they invest in. For example, you can invest in risky, non-commercial grade bonds, also known as junk bonds. Or you can invest in short-term bonds, which are much safer but return much less. There's no such thing as the 'average bond'.
So, let's go for somewhere in the middle. Let's go for 3% return, after fees.
Now, it's fairly simple math. You want $3,000 a month, or $36,000 a year. To generate that sort of return, you'd need to invest $1,200,000. If we are more optimistic, we could go for a 4% return, after fees. That reduces your investment to $900,000.
Note that it would almost certainly not make sense to invest all that money in bonds. Instead, you'd want to invest in a mix of stocks and bonds. This could likely reduce your risk while increasing your expected return.