How to travel by bus or train - Memmingen to Bavarian Alps

Hey travelers,

I will be flying to and from Memmingen on the 22nd of May to the 25th. I wanted to go hiking and potentially camping in the Bavarian Alps.

I will not be renting a car and I was wondering if there is accessible public transport I can take. Please give me some suggestions how to go about this journey. I am excited to read your recommendations, so please share any knowledge that could be helpful, including transport and hike suggestions!