Syvia, invitating and welcoming works for me. It is indeed more then 'simply being available' - its inviting people to enter into a relationship, a dance, a conversation, a mutual silence (add to taste ...)
The critical threshold for a Montessori 'Directress' as well as a Montessori parent is to welcome, show, and then to step back and put your hands behind your back, and shut up, so that the learner can figure out if the invitation and welcome articulates with what they need at that point in their own development (or not), and get on with it (all happens intuitively and implicitly if the welcome is open enough). Some people (Directresses and parents) find this almost impossible to do.
An open welcome also welcomes a 'no thank you' response - as and important part of learning. The young bird in your picture might not be so lucky!