The National Trust for Scotland, which developed the focal point in the battle's 700th anniversary celebrations, said it wanted to test the market, with flyers sent exclusively to people who had signed up to its dedicated website.
The real push ahead of the launch on March 1 is yet to come, the NTS said after Monday's tally.
The trust said it expects the centre to be a heritage hit and that more then 4000 children are already booked in for school trips. All places for the current academic year are taken after 700 school children earlier "road-tested" the facility, where a main attraction is its 3D Battle Game.
Around 6000 bookings have been made through the travel trade, including 3000 from North America as well as Germany, Scandinavia and the UK.
David McAllister, Battle of Bannockburn Project director who runs the centre, said the facility is the only one of its kind in the world.
He said: "International interest in the new centre has resulted in an impressive 10,000 advance ticket bookings through travel trade and education groups even before it has opened its doors or kicked-off on its marketing campaign.
"Over the last weekend alone, we have had over 500 firm bookings as a result of an emailed flyer announcing tickets are now on sale to the public, sent at the end of last week on an exclusive basis to people who had registered via the website."
He added: "We have deliberately kept things low key to enable us to have a 'soft' opening."
The news comes after the flagship Battle of Bannockburn celebrations had to be cut from three days to two in June, with only 2000 of the 45,000 on offer tickets sold by last month.
Tourism body VisitScotland took over the two-day event, which had its budget cut from £950,000 to £650,000, from NTS.