I've taught a lot of different conversation classes and the one-to-one classes have usually been the hardest. The best thing I've found is to find material that matches up with your student's interests (instead of trying the conversation textbook gambits) - whatever she likes reading about or talking about in Polish - and use things like magazine or newspaper articles as something to talk about. For each class you should cover vocab. topics such as agreeing/disagreeing, changing the subject, interjecting - all the vocab and expressions she needs to express her opinions and keep a conversation flowing.
You could warm up by talking about something she did recently, or something she has heard about, then review the conversation vocabulary and practise it, and then discuss the chosen article/s. After you've found some articles yourself then you could encourage her to bring her own pieces to the class so you can discuss the vocabulary (check she understands meaning in this context and others, how it affects the tone of the article, it it's sarcastic or not etc.) with her as well as the subject. You can also roleplay different situations and discuss points such as taboo subjects, small talk do's and don'ts - meeting someone for the first time, talking with someone you don't know very well, workplace conversations etc. You can also develop her debating skills by picking out the usual topics and assign her, or let her choose, a "for" or "against" role.
Lots of converstions these days aren't exactly deep discussions and focus a lot on what's happening on TV and in the newspapers, the usual rubbish about celebs or Big Brother for example, so she needs encouraging to be more aware of the culture as well as the language. An easy subject to discuss at the beginning is how she feels about life in England and how it compares to life in Poland. A subject like this usually gets the quietest student to suddenly have a lot to talk about.
Hope this helps, and good luck with the classes