As I understand from an online dictionary, "to put out for someone" is to make an effort for someone, and in that sense, I'd certainly use "molestarse por alguien", but only if it were another person than me:
- ¿Te molestaría hacer esto por mí?
- No sé si María quisiera molestarse en ayudarme.
- Ya que se molestaron en ayudarme, les agradezco por sus atenciones.
...
However, and although this is probably a regional prejudice, saying "yo me molesto por ayudarte" sounds conceited and rude, because it implies that you are actually being bothered by helping someone. So, I'd suggest widely different formulations:
- Lo haría por ti, porque eres mi amiga.
- Yo haría el esfuerzo por ti, porque eres mi amiga.
- No me molesta hacer esto por ti, porque eres mi amiga.
...
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