The info i have given you has all been from the Full indexes on Ancestry - I dont have a subscription, they are free for all to view!
So - for the children of the Bickerdyke girls it is a case of trawling thorugh year by year, and quarter by quarter within each year looking for children with the appropiate surname with 'mother's maiden name' listed as Bickerdyke. (If you want help -just give us the surname and date of marriage)
If you have broadband it really doesnt take that long, though I understand if you dont, it does.
My research days started before this was online, and you had to take a trip up to London and physically trawl throught the index books (that these images are scanned from) - so anything is quick and easy in comparison! And before censuses were indexed - hours and hours of winding through films and films of censuses looking for a name.... Oh those were the days!