Check out this link on You Tube, Dick Ritger's bowling Videos, Done in the 90's but great information, he covers just about everything, a little cheesy but helped me with my lift and release problems.  Hope this helps.

 

If Link doesn't work Dick Ritger feelings of bowling starts at Volume 1 part 1

 

Amen. It could be that this drifting phenomenon has other/deeper sources and is just the visual result of a flaw, e.g. in the pushaway or a timing issue. But, as se7en mentioned, if it actually does not hurt your game or forces you to make muscled corrections or other weird stuff which causes inconsistency, I'd leave it alone. Or, to be sure, try to check if the drift is causing some trouble. Maybe a local coach or a neutral, experienced player should take a look at your overall delivery.

 

A friend of mine also used to drift a lot - he had a rather short approach and would open the shoulder to generate momentum, and simply had to make a side step to compensate for the swinging pendulum masses. He'd do this very consistently, though, and it did no executive harm - even though my club's youth coach frequently mocked at him because it looked like a "power player" impersonation. 

DizzyFugu - Reporting from Germany
Confused by bowling? Check out BR.com's vault of wisdom: the unofficial FAQ section

Drifting and stepping to the right as you start to execute your slide are two different things and you need to nip it in the bud as it can get worse(stepping further to the right) over a period of a seasons without you realizing it making you inconsistent. The one step approach is a great drill to practice and will correct this over time. Remember that muscle memory is hard to overcome and will take a period of time as your mind will want to revert back to how it's use too doing it especially under pressure. Just stick with it and it will payoff with the approach you want. Good Luck.