The usual voluminous terms and conditions, yet they still can't be clear about how many times the bonus is awarded. Here's the relevant condition:
5. When Eligible Participants have converted at least the minimum number of Hotel Points awarded by any of the participating hotels/hotel loyalty schemes they will qualify for 2,000 bonus BA Miles which will be credited approximately 6-8 weeks after the conversion. The 2,000 bonus BA Miles will be credited by BA. All BA Miles are issued subject to Executive Club Membership terms and conditions.
'at least the minimum number' - OK.
'any of the ... schemes' - er, one or more than one, once or more than once?
At least they say 'The 2,000 bonus BA Miles will be credited by BA.' This is clear.
Last time, when there was a bonus of 500 BA Miles for SPG members, the bonuses were not awarded as promised but in dribbles some months later. And the dreaded BA 'help'line maintained we should contact Starwood as it was their promotion, even though the offer had online transfer reached via a link from ba.com

.