Ignore her while she is telling you in plain text that she wants to fuck? Dude, it's like refusing to take money on your payday... sad
You don't have to jump on her, but at least be friendly.
You don't have to use game in front of her BF. If she sent naked pics I suppose she means business and isn't just messing around with your self esteem. IMO she just wants to find someone (who is not living near her, cause maybe everyone knows each other at place where she lives) to fuck just for variety behind her BF's back, like you said "once a month or so". And if it's not gonna be you it will be someone else...
Looks like a legit cheater. Clever cheaters don't shit where they live
I would have tried to meet her somewhere when her BF is not around, kinda for a coffee/lunch or such "non-romantical" time of day, to avoid some legit assumptions by her BF

And there should be an Isolation possibility for a case if things get "hot", maybe a car or a hotel.
Text game is good for newbies so they have time to think about reply, I'd personally prefer to call (when BF is not around her) and use my voice to make her more interested.
- jettiger