How bitter? Bitter compared to the iceberg you buy in the store? Or tough, waxy, harshly bitter?
Fresh lettuce is more bitter than lettuce that has been stored cold, the compounds that give lettuce its flavor, and bitterness, are mostly metabolized withing a few days. So try putting it in the fridge for a while first and see if you like that better. Also, the type and variety make a difference. Iceberg is nearly all water, very mild, a little sweet. Leaf lettuce is the most healthy, and usually the most bitter. Romaine, bibb are somewhere in between and with all the various crosses available sometimes all of that goes right out the window. Some varieties are bred for low bitterness, but keep in mind they may have other problems. Some of the sweeter ones that come to mind are Sucrine, Falstaff, Mayan Jaguar.
If it is waxy, where it squeaks when you rub it between your fingers. That is from stress, most likely water stress. When you transplant, it will need water like every day it is above 75, not much water, just enough to wet the root plug. Then maybe every 2-3 days, depending on how fast your soil dries out, on hot days it likes a couple minutes of being sprayed down with a hose during the hottest part of the day to cool it off. When they are closer to harvest, having filled in the space, they might need water every day because their leaf mass uses it quickly, but are also more likely to develop rot issues from staying wet for too long.
Or, it might not have enough nitrogen, slow release organic sources that don’t leach out with the frequent waterings work best. Also, pH might be too low. Adding compost is a pretty good no think remedy, lettuce will happily grow well in straight compost for me.