Sneak in, one-shot with arrow, sneak out. IMO it's an unfortunate bit of business that has to be done in order to do anything with the DB at all, including destroying them (which I find rather irksome), so I'm not interested in anything but getting it out of the way as quickly and quietly as possible.
Surprised you had trouble with the guards, though, as IIRC there is no bounty assessed for this particular killing no matter how and when it's done. I've done it by walking up to her in full view of everyone else in the orphanage, including her assistant (who is not pleased about it at all, in contrast to the kids) and then walked right back out in broad daylight and gone about my business and never had a problem.