A quick look at the census records (be sure to look for both Alden and Francis) will get you back a few more generations, and then there are some Trees that go back to the Richard BARTLETT 1575-1647 that John mentioned, although not through Josiah, it's the same line.
If you want to really prove the lineage, you can join our BARTLETT-DNA project. It's ten years old this year, with over 240 participants. We have matching DNA for Josiah's line, and it is well documented by DNA and John's Tree. The DNA test is a cheek swab, so easy and painless. The company we use is www.familytreedna.com A living male BARTLETT must take this test. Here is the link, if you are interested: http://www.familytreedna.com/surname_join.asp?code=C45062http://www.familytreedna.com/surname_join.asp?code=C45062