The real issue is to find out, why she does not want you to be away from work. It could be that she feels you or your research are not yet ready or that she know you are on a though schedule with your project anyway. The reasons might be good or not, they might be valid or not.
Talk to your supervisor to find out more about the reason. Maybe you can address them or convince your supervisor, that you should attend at least a conference per year.
If money for travel expanses is rare, you can apply for travel grant, apply to conferences nearby or pay them from your own pocket. The experience might be worth the money.