The £5 note - the first polymer note the bank has produced - was designed by 13-year-old Dundee schoolgirl Kayla Robson.
The note will be a limited edition, with circulation limited to 50 notes to make it popular with collectors and raise more money for the charity.
Pudsey Bear makes a guest appearance on the note, raising a Saltire flag.
The serial numbers on the notes will also be unique, with the first 40 notes using the code PUDSEY01 to PUDSEY40, while the remaining ten will be personalised to buyers.
The bank said given the rarity of the notes it is likely they could sell for hundreds of pounds each when they go under the hammer at Spink's in December.
Annette Barnes, Bank of Scotland's retail managing director, said: "This new five pound note is brighter and bolder than most other banknotes in circulation and really brings to life what BBC Children in Need means to so many people.
"Kayla did a fantastic job with her design and I am delighted to see how we have been able to incorporate it into our first polymer banknote."
Bank of Scotland has unveiled a polymer banknote which will be auctioned off to raise money for Children in Need.