Heya mbuk04, what you can try is SUPERSET each bicep routine with the tricep routine in order, by a superset i mean you compelte the bicep routine and then immediately commence on the tricep routine, something like ill show you below your midified workout to inlcude supersets.
SupersetPart 1
Barbell curl - 4 x 4-6 reps
Close grip
bench press - 4 x 4-6 reps?? I would probably do Skullcrushers 4 x 4-6
SupersetPart 2
Hammer Curl - 4 x 4-6 reps
lying french curl - 4 x 4-6 reps
SupersetPart 3
Preacher Curl - 4 x 4-6 reps
1 arm overhead - 4 x 4-6 reps
And the deal with this is forexample in supersetpart 1, you perform 1 set of the barbell curl and start immediately on the close grip benchpress / skullcrusher and then have a breather, then continue the second time around barbell curl then closegrip / skullcrushers immediately then take a breather once you have done the 4 supersets for SupersetPart1
now start SupersetPart 2 in the same manner and part 3.
Hope it helps give you an idea becuase i think that training revolves around Intensity in the shortest amount of time, so supersetting is great in that respect