Bedell’s great-grandfather bought Hamerton in 1565.
Returned for Hertford in 1626, presumably with the support of his brother-in-law, Thomas Fanshawe II*, who had represented the borough in the two preceding Parliaments, Bedell was appointed to seven bill committees, whose subjects included the oaths of accountants (11 Feb.), the removal of scandalous and unworthy clergymen (15 Feb.), the provision of work and religious instruction in gaols (8 Mar.), and restrictions on clerical magistrates (10 March).
Huntingdonshire re-elected Bedell to the Short Parliament in April 1640, by which time his motive for standing was probably to obtain respite from the demands of creditors. He had become indebted principally, it would seem, as surety for Oliver St. John II*, and managed to secure a grant of protection for six months in May 1640, but was outlawed when it expired.
