Like most guy's who come on here you did not post rep or sets schemes, which can make quite a difference in a training program...anyway moving on.
If you have an overwhelming need to do dips than drop the BP and only do dips. But experiment with different grips/hand spacings. If training on a "V" bar than a greater opportunity is given for extra wide to narrow and knuckles facing forward (excellent pec builder, also triceps) . May also including keeping the body straight up (180 degrees), which can be a superior tricep builder. Just my view, but I consider all around dipping styles better than benches.....for me anyway. May also want to keep it, as with any other exercise/muscle group, to twice a week. And start a workout with the heavier compound exercises in first order
Might suggest, based on your 3 day a week plan:
Monday- DL, lat pulldowns, dips & biceps
Wednesday- Squats (I see your not a leg man...so once a week for these?), shoulder press and ab work with a 8 to 12 rep range, adding weight as advancing.
Friday- DL ...I myself would do Romanian DL's... more of a combo of a SLDL & GM'ing which hit the hams, glutes, lower/mid back lats & taps. Please be advised to check out some training vid's if you decide to use this exercise. And start learning it with very light weight at first.It will help greatly with the regular DL & saquat
GM'ing..if choosing to do Romanian DL the GM will not be needed. Next will be dips followed by biceps. Nothing special fpr the triceps, because all the dipping should take care of them. Good Luck.