You can get bug nets that can be used with a tarp like these:

https://www.rei.com/c/bug-shelters?r=category%3Acamping-and-hiking|tents|shelters|bug-shelters&ir=category%3Abug-shelters

This one is made with insect shield and should be very effective against Ticks, Chiggers and Mosquitos:

https://www.rei.com/product/849594/sea-to-summit-nano-mosquito-pyramid-insect-shield-net-shelter

I started out tarp camping many years ago and seldom had problems with bugs and never had problems with mice. That said, it depends on the season and the location. In peak bug season, a tent or bug net is desirable. A tent will not provide as much ventilation as a tarp and may be uncomfortably hot. In colder weather bugs aren't as much of a problem, except for ticks. When the ticks come out, probably this month or next, they will be thick. You are more likely to get them while hiking, but could pick them up at camp. Here in Illinois, Insect Shield has been the most effective deterrent for me. Socks treated with Insect Shield (Permethrin) have stopped almost all of my ticks and chigger bites. Overall, the choice of tent or tarp depends on where you are and what you want to do. In exposed country, tarps just don't provide much protection from wind, unless pitched right down to the ground. A free standing double wall tent provides much more protection, but at a weight and bulk penalty.