I have always wondered this question.
First I realized that all the founding fathers had British accents, then wondered what the generation or two in America after them sounded like.
I assume the older generation still had a bit of a British accent, and with the mass waves of immigration there was probably a ton of accents in the country. Was there a unique "American accent" at one point in the country's history?
And is the current American Accent just a bastardized version of all the other accents?
There wasn't a typical accent.
Also the founding fathers didn't have British accents, at least not as you're thinking of them today. The modern British accents are all innovative, and were not the same 200 years ago.
Adding to that, there wasn't a single British accent then either, so you would have had a good number of different accents even from people who were recently coming from the British Isles.
Adding to that, the huge majority of founding fathers were born in the 13 colonies and as such would not have had British accent anyway; they would have had something that was a number of generations separated from how people were speaking in England at the time. Some were born in England, Scotland of Ireland, but Alexander Hamilton was from the West Indies. James Wilson too was judged for having a Scottish accent (being one of the few born there).
Back to the heard of the question. There would have been a somewhat typical accent at least in terms of what characterised regions, but it would have still been wildly variable (as New England accents still are today). There would have been, for example, a Virginia accent, an accent typical for Boston, for Philadelphia. But the sort of regional variety seen in those today would have been all the more substantial in the late 1700s. It wouldn't have all been simply British. A long time had passed since 1630.
And is the current American Accent just a bastardized version of all the other accents?
Absolutely not. Not any more than the current dominant London accent is a bastardisation. All accents are the result of change, and often due to contact with other linguistic groups, but just as easily happening without that contact. No one speaks exactly like their parents. Non-linguists just aren't generally aware of the differences, being that they're fairly subtle.
Language is constantly changing. To consider any change to be the result of "bastardisation" just means the person making the characterisation isn't aware of just how much change is constantly going on everywhere in the world, even in their own home.
You may want to ask this at r/linguistics too! :)