David Cotterill grabbed the first before Bale set up Hal Robson-Kanu for the second.
Swansea winger Cotterill broke the deadlock on 35 minutes volleying home Robert Earnshaw's cross.
Following Cotterill's departure, the Clarets have leapfrogged Wednesday and are three places above them in 13th.
Cotterill is the fourth different boss at Meadow Lane this season, following Ian McParland, Kevan and Hans Backe.
Kevan, who worked with Cotterill at Stoke and Burnley, will revert to his former role as assistant manager.
Burnley have been without a manager since Steve Cotterill left Turf Moor by mutual consent on 8 November.
After leaving Whaddon Road in 2004 he returned to Kidderminster briefly before becoming Cotterill's first-team coach at Burnley.
BBC: Kidderminster's Mark Yates appointed Cheltenham manager
David Cotterill, Andy King and Ashley Williams all scored first senior goals, with Joe Ledley hitting a penalty.
Cotterill led Town to the Football League for the first time in 1999 and is their most successful manager.
Cotterill joined County on a short-term contract in February and in April his side clinched promotion to League One.
Cotterill, who joined the Magpies in February, said the decision to go was "one of the hardest of my career".
But when Paul McShane was ruled to have tugged down Welsh sub David Cotterill it gave Koumas the chance to level.
Cotterill is one of only 12 English coaches to hold the Uefa pro licence, the highest coaching qualification in European football.
Cotterill is the third manager to part company with County in the past eight months, alongside Ian McParland and Hans Backe.
Cotterill started his managerial career in 1995, succeeding Lawrie Sanchez at Irish side Sligo before taking charge at Cheltenham two years later.
Cotterill struck from the penalty spot after being fouled by Charlie Lee.
Toshack also praised Swansea's Cotterill, Leicester's Andy King and Blackpool's David Vaughan.
Wales boss Toshack made five changes at half-time, with Myhill, Ramsey, Sam Vokes, Carl Fletcher and David Cotterill all coming off the bench.
In retrospect, Cotterill would have been better off proving himself further at Stoke rather than gambling on a move to the big time.
"It was the draw of playing, " Pack told BBC Gloucestershire, after arriving on a season-long loan deal from ex-Robins boss Steve Cotterill's Portsmouth.
But Wales were creating chances themselves down the wings, with Bale on the left and Cotterill on the right bombing forward when prompted by Ramsey.
The question for Cotterill is whether he has learnt anything from his spell at the Stadium of Light that will make him a better coach.
After taking Cheltenham into the Conference and up to Division Two, with the FA Trophy won en route, Cotterill was rightly tipped for the top.
The visitors threw on Argentine Julio Arca on the hour to add some steel to their midfield, while David Cotterill replaced Mark Gower for the Swans.
Ruddy gave away the penalty in a one-on-one with Swans striker Scott Sinclair but brushed himself off to tip David Cotterill's spot-kick on to the post.
In one such attack Cotterill, reaching the byline before pulling the ball back, fashioned a chance for Edwards, but the Wolves midfielder saw his shot deflected wide.
Ched Evans took over up front for the hard-working Vokes after 62 minutes, while defender Lewin Nyatanga was sacrificed as David Cotterill beefed up Wales' attacking options.
But Cotterill, whose first match in charge will be the home game against Hereford on Saturday, has not held a managerial post since leaving Burnley in November 2007.
Koumas scored his second from the penalty spot in the 89th minute after McShane's clumsy challenge on Cotterill to give Wales some slight comfort from a disappointing campaign.
The home side eased the anguish of the dumbfounded Liberty Stadium crowd on 23 minutes as Van der Gun directed goal-ward a header from a David Cotterill corner.
应用推荐