As a DM I gave our dwarf cleric a bear cub as a companion, what can I do?

So I’m with 2 PCs, playing D&D essentials kit. Most of the time we follow the plot, add some extra things there and here and of course doing some improve. I try to stick to some of the rules but not always, to make it more fun.

The PCs recently encountered a big brown bear and killed it. A bear cub appeared and they managed to persuade the cub to go with them and they have it now. I applied wolf stats to it (didn’t give them the card yet, should I?). So now I’m thinking what this bear could do. I do not want to mobilize it as a fighting companion but make it more passive in battles and just help them with it’s perception and some other goodies.

I was thinking:

  1. Make the bear cub not grow with time, but rather give them an item to make the bear stronger in terms of constitution.

  2. It mostly follows them and will not run away on it’s own unless it’s in life threatening danger.

Edit: Question: Do my two points make sense and what stats should I include any other mechanics that would work with this relationship between dwarf and bear? Should I allow mounting of the bear once it grows?

edit2: what stats and info can i reveal to my PC?