Here's my outline for mounting mechanics. I'd like these to be engaging and unique, and fit the style of Grounded as closely as possible.
The Ladybug seems to be the perfect ride, but she also has some fight in her. Once tamed, she can be used as a pack mule, or a war mount. This starts by choosing a saddle, which will either be a War Saddle, or a Pack Saddle. The war saddle will be large, and consist of tough outer armor, and a comfy spot for her chosen warrior. The pack saddle sacrifices comfort for storage, allowing you to attach acorn chests, as well as pile on grass planks or weed stems. Initially, she will be limited in her abilities, but by accessing a menu, you will be able to provide her various cooked meals to upgrade her stats, such as carry capacity, max health, movement speed, and max stamina.
The saddles themselves can also be upgraded, but you must be sure that her carry capacity allows for this. The pack saddle should be unlocked around midway in the game, allowing you to carry large quantities of supplies as your base ideas become more ambitious. The war saddle, however, will be a late-game unlock, but you can swap these saddles at any time, so be sure to tame that Ladybug as soon as you can. Keep in mind, however, that saddles can only be carried on your shoulder, and can only be stored on grass pallets.
The Bee is a dutiful and speedy insect, adept at flying high above the action, and all across the yard. Because of this, it seems only fair that they aid you in your quests, given you can earn their favor. In order to do this, you must construct an offering, which looks a lot like a flower. From there, you must keep it chock full of that sweet, sweet nectar. If a bee stumbles upon your offering, she will return there the next day at the exact same time. Be sure to arrive on time, and you will slowly gain her trust. Upon the 3rd consecutive day, after collecting the nectar from your offering, she will begin to follow you. You have until nightfall to offer her a Petal Bow, which will allow you to keep track of her as she buzzes around the yard. You have now tamed a bee! But you aren't even close to riding her yet. To do that, you'll need a Sleek Saddle, crafted by rare end-game materials. You also need to continue to maintain your offering, as well as spend time with your bee to increase her trust to the maximum level. Only then will she allow you to place the saddle, and finally ride off into the sunset.
There's no choice for combat when riding a bee. Not only is she non-confrontational, but she definitely doesn't want you to get hurt! Ain't that sweet?