Lilly:
She should NOT give ANY notice until an offer with a firm start date has been extended to her.
She will need to compare the offers and the jobs side-by-side. Which one suits her better, benefits, hours, location/commute, etc. No one can make that decision for her.
Does she "owe" the company loyalty? As a recruiter? I would love to say YES!!! But really? It's a dog-eat-dog world. Gone are the days of staying with companies for decades or even into retirement! Heck one of my candidates has been with a HUGE company for TWENTY-FIVE YEARS - yep 25 years - and he's been given 4 weeks notice. That's IT. He started with them as in intern in college - he's 45 years old....it's the ONLY company he's ever worked for. And he's scared. Nervous. And so many other things - as the company is "employee owned" and did not do the typical 401K plan...and they are treating him as if he hasn't spent 25 years with them.
She should NOT burn any bridges. She should continue to do the job she has to the best of her ability - she owes them that. She should try to interview with company B either before work or after work...maybe even during lunch....it would be a slap in the face to take a day off to interview if she's only been there a few weeks....it would suck if she called in sick and someone saw her somewhere....or she gave notice after taking the day off...that would be burning a bridge...
Company B is NOT a sure thing. So if company B has a job that is more along her career field - then she should pursue it. She won't have a "what if" in her life. She will know she tried. If she gets it - GREAT!! IF not? She Tried.
Good luck!