If you want to craft some arrows and start taking out bugs from afar then you're going to need to get yourself some Thistle Needle. It isn't too hard to find, but you might have to make a pretty good run across the garden to find it.
You can get Thistle Needle in Grounded by chopping down Thistle plants. These can be found by looking for the bright purple flowers that bloom from them. Try to get somewhere high and look around for one, then run on over and chop at it to gather the needles.
The thistle plant is just one of the purple blooms you'll see in Grounded. So, make sure to find the one that looks like the image shown above! There's at least one spawn you can find near the oak tree where you find acorns and grubs. Once you find one of these, you will need to take out your axe and chop at it. Each swing should get you some Thistle Needles!
Once you've gathered up plenty of these, you'll want to create yourself some Arrows to attack bugs from far away! You can also make a Spiky Sprig which is an upgraded weapon that does quite a bit more damage than the spear.