Merhaba;

If someone asks me on facebook that "bana ulasabılırmısın?" does it mean that "Do I have access to her on facebook" or it means that "Can I call her on phone?" which one is correct.

I would be very glad if you help me with that.

Thanks

My try: You can reach me

But wait for others.

The verb ´ulaşmak´ has several meanings but I think, here, it means ´to find´.  Therefore ´ulaşabılır mısın?´ means ´can you find´ and ´bana ulaşabılır mısın?´ is ´can you find me?´.

So you were right with the first one, she is asking if you can find her on facebook.

Cok tesekkurler

can you communicate with me ?

might be another possibiltiy

Ok - or ´contact me´ or- with ´telefon´ - ´reach me by ´phone´.  So, maybe as the OP says she got the message on facebook, her friend does mean ´can you ´phone me?´  I didn´t realise ´telefonla ulaşmak´ was a possibility earlier!

Most likely they mean if you can call them

for example we mostly say "mesajımı alınca bana ulaşabilir misin?" which means "could you call me when you get my msg?"