There are so many differences across the counry that impact this topic!
I agree that waiting to bring practical experience to your advanced degree study is important. You may not have a choice in determining these dates, however, as different states have different requirements. For example, a teacher in NY needs to complete his/her Masters within 5 years of receiving the undergraduate degree in order to gain/continue employment. I advise looking into this, in your state, as it could have a major affect on your own situation.
With regard to the $$ issue of having a Masters: now, many districts will only pay for a limited number of years of experience, and may or may not include the acquisition of an advanced degree. Perhaps the most important reason to “stay put” is the uncertainty of the job market and the longevity of music positions in school districts (think senioroity!). It would always be up to you to accept the offered salary that might not include pay for the masters.