First of all..... ditch the bipod and use sand bags...
Second..... get a few business cards and pack them under the barrel at the tip of the forend.. so they exert some upward pressure on the barrel..... essentially stopping it free floating and creating a 'pressure bedding'.
Use the rounds that shot the best and shoot a group of 3....
Then report back the results.
I did the same with my rifle after having a lightweight sporter barrel fitted.... I was unhappy with the groups... they were inconsistent. I ditched the bipod and did the business card thing and my groups shrank from 2 and half inches to around inch and a half... and remained consistent from cold. Any more than 3 shots in succession caused the barrel and mod to get very hot.
I then full length bedded the barrel with more pressure on the tip of the forend and it now shoots hornady factory into3 quater inch 3 shot group off a sandbag. My stock is a mcmillan and the barrel is a lightweight sporter 20 inch lothar walther fitted by Steve kershaw..... and it was very freefloating until I tried the forend tip bedding. I torque my stock screws 40 inch pounds.... which is the general recommended setting.
And before the experts start spouting on about point of impact shift through stock warpage etc....... that applies to wood not synthetic.
Try it before you give up hope..... lightweight barrels are whippy and more often than not react better when that movement is tamed consistently.