I have loaded a few of the 125gr Berry's FP plated bullets using Bullseye. These loads had no issues, so you can probably go lower. Lyman 50th lists a 125gr JHP load starting at 3.2gr of Bullseye.
38spl, SP101, 3"
Case: PMC
COL: 1.423"
Berrys, 125gr, FP, Bullseye, 4.0gr, WSP
Average: 715
ES: 56
SD: 21.4
Force: 142
PF: 89
Velocities: 684, 706, 723, 725, 740
Grouping @ 7yd: 0.61"
Test Date: 10/21/2018
38spl, SP101, 3"
Case: PMC
COL: 1.423"
Berrys, 125gr, FP, Bullseye, 4.2gr, WSP
Average: 719
ES: 114
SD: 45.1
Force: 143
PF: 89
Velocities: 658, 698, 718, 772, 753
Grouping @ 7yd: 0.85"
Test Date: 10/21/2018
38spl, SP101, 3"
Case: PMC
COL: 1.423"
Berrys, 125gr, FP, Bullseye, 4.4gr, WSP
Average: 795
ES: 42
SD: 16.1
Force: 175
PF: 99
Velocities: 770, 794, 793, 812, 806
Grouping @ 7yd: 0.71"
Test Date: 10/21/2018