Right wing Dodge played the full 80 minutes, while Cole was given 68 minutes at prop with Shaw playing just five minutes less on the blindside flank.
Sale Sharks No.8 David Tait celebrated his first start for four months with a try in each half, with replacements Tom Parker, Matt Cox and Hugo Ellis adding further scores for the English.
"I was happy in the end but as a side we need to develop our understanding of how to build a score," said Redman. "There were aspects of the first half which were outstanding and the territory that we had was a huge plus but I was disappointed with the fact that we lacked patience at times.
"In fairness we had a lot of disruption this week but the guys who came in did us proud. It was a good start but we know that we have to do better this season."
Captain Danny Care of NEC Harlequins, who bruised a hip but should be fit for next week's clash against Italy, added: "We got off to a great start but it got a bit frustrating in the middle of the first half when we were constantly piling on the pressure and couldn't break through. But eventually we were happy."
The Rugby Football Union, along with the other Home Unions, have switched from U-21 (with England having won the Grand Slam last season and also in 2003/04), to an U-20 age grade, with France and Italy due to follow suit in 2008.
England are back at the Recreation Ground to face Italy U-21 next Friday. They then meet Ireland U-20 in Athlone (February 23), France U-21 at Northampton (March 9) and Wales U-20 at Newport (March 16).
England U-20
F Neale (Saracens, rep J Tirrell, Saracens 70); O Dodge (Leicester Tigers), A Thompstone (NEC Harlequins, rep C Gower London Irish 77), A Powell (Saracens), S Kuadey (Sale Sharks); S Jewell (NEC Harlequins), D Care (capt, NEC Harlequins, rep T Parker, London Irish 48); D Cole (Leicester Tigers, rep C Beech, Northampton Saints 68), M Mullan (Worcester Warriors, rep R McMillan, Gloucester Rugby 75), J Forster (Gloucester Rugby), D Attwood (Bristol Rugby), P Hoy (Northampton Saints), A Shaw (Leicester Tigers, rep M Cox Worcester Warriors 63), C Pennycook (Bristol Rugby), D Tait (Sale Sharks, rep H Ellis London Wasps 68).
Scorers: Tries - Tait (2), Parker, Cox, Ellis; Cons - Neale (3).
Scotland U-20
C Goudie (Stewart's-Melville FP); D McCall (Edinburgh Rugby & Stewart's-Melville FP, rep C Anderson Melrose 77), R Hutton (Hawick, ), G Hogg (Border Reivers & Hawick), A Easson (Edinburgh Rugby & Stewart's-Melville FP), A Grove (Worcester Warriors); C Ferguson (capt, Edinburgh Rugby & Dundee HSFP), J Hunter (Glasgow Warriors & Hillhead/Jordanhill, rep M Bringhurst, Edinburgh Rugby & Watsonians 60); A Dymock (Edinburgh Rugby & Dundee HSFP), P MacArthur (Ayr, rep F Wilford Sheffield Hallam University & Rotherham Titans 58), K Traynor (Edinburgh Rugby & Boroughmuir, rep B Pow, Hawick 44-49), W Lipp (Watsonians), S Turnbull (Edinburgh Rugby & Heriot's, rep G McGilchrist, Tynedale 62), D Lambert (Heriot's, rep B Pow, Hawick 44-49), R Grant (Border Reivers & Gala, rep D Levison, Dundee HSFP 34), R Vernon (Border Reivers & Stewart's-Melville FP).
Sin-binned: Dymock 39-49
Scorers: Try - Bringhurst
Referee: Peter Fitzgibbon (IRFU)
Attendance: 5,008
