Burdett in America
A good place to start is with sources that have been published and indexed by other historians - since they have done a lot of the hard work for us already. There is a published list of 'persons of quality' who sailed to New England in the 1630s (created by the English monarch, who wanted to know who was leaving the country).Unfortunately, Burdett's name does not appear. This is not, however, that unusual. Every piece of evidence has its gaps, and failing to find something does not mean it wasn't there, only that it wasn't recorded.
'Every piece of evidence has its gaps ...'
If we can't see Burdett leaving England, perhaps we can find him on the other side. And, indeed, consulting a 1635 list of 'freemen' in Salem, New England (published by the New England Genealogical Society), we find mention of 'Mr George Byrditt'. Now, we cannot assume absolutely that this is the same man - but, in an age where spelling was rarely consistent, 'Byrditt' and 'Burdett' are sufficiently similar for us to think this could be the man we are looking for.