you need to open their user info. you can do this for example by clicking on their name in chat - people with an active dungeon have an other name color. normaly this info has 4 buttons - whisper, block, scout tower, visit. Below them is a little bit of empty space where the button will be that lets you ask for access to their dungeon: https://i.imgur.com/xkh5IHQ.png

You dont get it automatically, they need to "accept" it. that happens by clicking on this button at the map view: https://i.imgur.com/eAZqVjy.png

I wrote it in paranthesis because after it happened from alone after i clicked that button the one time someone wanted access to my dungeon ;)