Bedwell joined
Swindon Town as a child, making his way through the youth ranks with the
Wiltshire club. Bedwell was given a first team squad number at the age of seventeen – when still a part of the youth set-up – acting as back-up to deputy
Phil Smith, when first-choice keeper
Mattia Lanzano and third-choice Mark Scott were both injured at the start of the 2011–12 season. The arrival of
Wes Foderingham prevented Bedwell from keeping his place in the starting sixteen but at the end of the season – though Smith, Lanzano and Scott were all released – Bedwell was offered his first professional contract, and he signed a one-year deal. Ahead of the 2012–13 season, Bedwell was given number 30 shirt. On 2 September 2012 Bedwell made his first team debut for Swindon in the 4–1 loss at
Preston North End. With Swindon losing 2–0 early into the game, Town manager
Paolo Di Canio decided to substitute first-choice goalkeeper
Wes Foderingham for the rookie Bedwell. At the end of the 2012–13 season, Bedwell's contract was extended for a further season. Bedwell was loaned out to
Banbury United in September 2013 to gain first-team experience. After making thirteen appearances, Bedwell returned on loan. In late April, Bedwell rejoined
Worcester City on loan for the second time this season. Bedwell was among ten players to be released by Swindon Town on 2 May 2014. After his release by Swindon Town, Bedwell rejoined
Banbury United on a permanent deal and was an ever-present in the side. However, following Banbury's relegation from the
Southern Premier Division in 2015, he joined
Southern League Division One South & West side
Didcot Town in June 2015. ==Career statistics==