As has been mentioned there are Internet based BBS systems. I really don't know about Amiga ones, but if you are a C= 8bit user there are plenty that might be of interest and the experience is the same as the old days. Q-Link is back and you use the original software to access it. There are quite a lot single line BBS out there also.
Once you get set up, the method for access all these are the same. Use same old terminal software, hear the same old modem dialing sounds. BBS experience is the same. The Sysops of these boards are dying for users.
None internet connected? That will be though to find.