If a girl decided to take the initiative and offered you a date first, then she definitely does not take courage. However, if you do not share her desires, then the girl will have to refuse.
Do you like her, but ahead of you with such a proposal? You should not take her initiative with hostility - the girl did not want to offend you at all, she simply showed excessive independence and, perhaps, hastened events that were already destined to happen, but a little later. Admit it - you yourself wanted to invite her, she just noticed your sympathy and did it first. There is nothing reprehensible in women's initiative.
However, if this is a matter of principle for you, then make it as delicate as possible to the girl that you are more conservative and think that the invitation should come exclusively from the man. Try not to catch a woman's pride with such a refusal, otherwise in the future the girl will react sharply to your proposal.
If you do not like the girl and you do not want to have a closer acquaintance with her, then the refusal may be more harsh, but also remain within the bounds of decency. Do not insult the girl, do not push her away - just make it clear that you want to leave your acquaintance exactly at the level at which it is at the moment, and do not want to change anything. No need to make categorical statements like "I never liked you", or "You are too ugly for me." At best, you will get a slap in the face, at worst, the girl will tell all common acquaintances what a boor and rude you are. If the girl does not understand the ethical refusal, it is still not worth going to shout. Tell her that, in principle, now you are not ready for any close relationship with the opposite sex, that you do not have time for this, or you feel a feeling of unrequited love for another girl. Pathetic excuses and attempts to escape by flight do not suit a real man either, so behave as confidently as possible and speak in a firm, calm tone.