If it looks rather downtrodden every time you leave it, that may be a good indication that it wishes to go with you. I would bring the idea up with this brionne. Offer to allow her to live with you and present her with a poké ball. Explain what it is and see how she responds. If she seems excited by the prospect of being with you full-time, then yes, catch her. If, however, she attempts to pull you towards the ocean or otherwise moves towards the water, then I would suggest seeing if you can visit her more often.
If you do adopt her, it seems you already know the basics of keeping a brionne. Just be sure that she has plenty of water in addition to the food and toys you already give her, and she should be fine on shore.
Best of luck, anonymous!