Is it better to call your new girlfriend or send a message?

It's simple. If you think you have a good chat, just call directly. Soon, it depends on how you communicate, how to make her feel that she has a common language with you, so as to enhance her feelings. If not, contact her by text message first, get familiar with it, let her accept you slowly, and then you will be sure. Then ask politely, and you can chat by phone, which will show more respect to her and she will understand what you mean.