Oakley said:

Adding on to what Asterism said, seeing as their response was more with how to save mush you already have, I have some advice on how to get mushrooms.

Some really great ways to acquire mushrooms are to explore. In explore, your wolves will find mushrooms, hunt, and battle animals for mushrooms.

Resources on how to explore more efficiently here: Explore Guide

Another way to make lots of game currency here is through art. I'm not sure how interested you are in art but this route is a really quick way to make lots of money, relax and make nice art. :)

I'm speaking from experience and for me, these are the best ways to make money. I hope this helps!

This^

What really helped me start saving mushrooms was setting a goal. My starting goal was 500 mushrooms a day. At the end of the day, I'd put it all in my mushroom hole. Now my goal is at least 1,000 mushrooms but I make way more than that because I know quick ways to make mush (which you will eventually learn what's best through playing). I recommend giving yourself a reachable goal and continuously reaching it, then increase that goal and so on. You'll eventually get into a habit and quickly save up mushrooms ^_^