We're 2 adults and one lap infant flying CW on the 787-8 between SJC-LHR. We wanted to get some kind of bassinet/carrycot (looks like there are two types on BA).

The phone agent put us in 1A/B, which doesn't show up as a bassinet position on aerolopa or BA. I questioned the agent twice and was assured we could have a bassinet. But I'm suspicious...
If not, any recommendation between 6A/B and 6J/K?

It seemed she was willing to put us anyplace with a bulkhead, perhaps there is always a place to attach a bassinet? Thanks in advance.