Hopefully you have your rig setup on some sort of casterboard or dolly. Before your set, your entire rig should be setup and patched, ready to go. When it's time, you roll your rig on stage, plug into the PA, set down your bass and bass stand, plug in your bass, tune, and your ready to rock.
I did most of my professional career with a 210 and approximately 250-400W and this was plenty for all but the loudest stadium gigs where gigantic side fills were provided. Under those circumstances I found it was best to turn my amp down so it didn't fight with the side fills.
My amp serves as my personal monitor, so it was not intended to fill the venue or stage with sound. Most of the time I used at least one speaker that was elevated to about waist level. When it was just a 210, it sat vertically on top of my rolling rack and had an extra DI wedged under the front edge to tilt it back and aim the speaker at my head. The whole idea is to make it possible for me to hear clearly while running my amp at the lowest possible level.
In my experience, putting bass in your foldback monitor is a crapshoot. Occasionally it can sound great, but most of the time the foldback monitor fights with your bass amp instead of integrating to produce a nice clear sound. The problem is monitors and bass speakers have different phase and group delay characteristics which can cause cancellation in the low end. It's also possible that the absolute phase is reversed, but I had a DI that allowed me to switch polarity, so this was not a problem for me.
I have also done a few gigs where I ran ampless and relied on foldback monitors. Having an amp gives you some degree of control over your sound. If you rely exclusively on the monitors, your experience is totally dependent on the quality of the provided gear, the skill of the audio techs, how attentive the audio techs are, and whether the audio techs are willing to give you what you want or not. I have been burned pretty bad running ampless when I relied on unfamiliar techs, so when possible I prefer to bring an amp. Having an amp allows me to adjust my stage volume and tone independently of the PA.
Regarding the need for your amp to provide sound for the front row. This is a mixed bag IMHO, but YMMV. First, if the PA can't send the bass to the audience in front of the stage, then it most likely will not be able to send the vocals in front of the stage, so the mix is going to suck period. Second, the need for you to balance is driven by the levels of the other instruments on stage. From the audio techs perspective the ideal situation is for their to be zero bleed from the stage. Obviously this is unrealistic since most bands use real drums. But guitars, bass, and keys all use amps and there is benefit in reducing the stage level of these instruments.
The problem is when you have two sound sources in separate locations, when the sound waves come together they will arrive at different phase angles, so you get irregular summing and cancellation that results in comb filtering. In order to reduce the effects of comb filtering, one of the sound sources needs to be significantly louder than the other.
Since the job of the PA is to deliver sound to the audience, ideally the PA should be the dominant sound source for as much of the audience chamber as possible. If the stage wash dominates in front of the stage, then the sound a few few back will be impacted significantly by comb filtering, because this will be the zone where the PA and the stage wash fights for dominance. IMHO better for the sound to be nice in this zone and allow the sound to suck in a zone that cannot be helped. Then again my rigs usually run front fills of an aux or matrix, so there is no dead zone.
My personal view if the PA is carrying all of the instruments: Amps serve as personal monitors and should be aimed consistent with this goal. I.E. the amp should be aimed to deliver sound primarily to whoever is playing through the amp. Theoretically this works because most people prefer to hear themselves louder in the mix than everyone else. So if you aim your amp at yourself and adjust it for a good balance, there is a better chance that everyone can get the desired level of "more me." Before turning on the PA, try to get a good acoustic balance where everyone's needs are met.
Foldback monitors should be used when you can't hear something you need to hear. For example if you can't hear the guitarist on the other side of the stage, then put a little guitar in your foldback monitor. Also, rather than cranking up your bass amp so everyone can hear it, have everyone put just enough bass in their monitor to suit their needs. Of course the problem is some people really like a lot of bass.
I will say running sound like this has worked really well when I am running a band, but it's not the way most people are used to doing it; so implementing this ideas sometimes faces resistance. Many people only think about how to get there own sound rather than how to best serve the audience's needs. They want to do things the way they have always done them and are resistant to trying new ideas. I try to take an approach that involves a compromise that ultimately serves everyone's needs instead of allowing one person's needs to dominate. Also, my belief is since the audience is our patron it's important to try and give them the best possible experience rather than focusing so much on our own needs and desires. I think many top professional musicians would agree with this philosophy.
