This can be quite tricky and all depends on the size of the venue.
Please bear in mind this is all from my experience and every bass player likes something different. Ill run through what ive done and currently do for different gigs. Also , I play in a funky souly band where the instrumental section is guitar bass and drums.
Small venues; I have the rig running on its own, no DI and no mic-ing. Have the bass louder than you think, only slightly though. I tend to boost the bottom end a little more as it dissapears when you get out to the crowd. Our singer always asks me to turn the bass down to but its just too quite then.
Also, we have the guitarist turn the bass on his amp down. Please dont shout at me, i can explain. In our band Soul Technique, Im the only one providing the bottom end, im in my own frequency range, its the same for the guitarist and so he needs to cut through much better. And because hes in a more general frequency band he doesnt need to be too loud.
Mid- big venues; The bass is DI'd, again the the bass is boosted to help carry the bottom end further into the crowd. I post eq the head and if need be ask the sound man to boost the bottom end on the desk. This doesnt sound muddy either as you can boost the upper mids a little or adjust where you play the strings. My monitering comes from my amp which im right next to. Dont be afraid to tell the sound man how you like your sound, theyre there to get your sound so make sure they do their job.
Once again, I cant stress that this is all from my own experience and its worked extremely well for me and Ive had nothing but compliments about the sound. And remember, your bass, this frequency will not over take vocals so it can be loud which adds weight and holds everything together like glue. Check out a Just Jack gig and youll hear how loud the bass is!!! Same for Elvis Costello, the bass is fantastically loud.
Hope this helps.
Dan