IME any time you are working in a legit pro studio, a short and cordial discussion of methods and goals with each player is expected at some point before tracking begins.
I wouldn't assume an engineer needs to be told how to do his job, but neither would I assume he is a mind reader. There are all kinds of styles and tastes. I can tell from one or two questions whether the guy gets what I am looking for, and a pro is going to want you to be comfortable and know that he respects at least the style of your music. Like if I was going to record a sort of post punk record, and I mention that I like the bass sounds on the original albums by Television, Gang of Four, and Joy Division, and I'll be using a head which is similar to a Hiwatt, I need to get some sort of knowing smile or something back.
If at the end of this exchange, the guy doesn't seem to get what the music is, or wants carte blanche to do whatever he normally does (like record DI only), as far as I'm concerned it is not going to happen with that guy and/or that studio. It's much better to find that out before anything is tracked.
I would emphasize that I've never even heard of an established pro studio refusing a basic, reasonable request like miking an amp (with an additional DI track). If the player's amp sucks or is too noisy, the appropriate response would be to suggest an available alternative.
Mic selection would typically be more up to the engineer, but I have to say, Beta 52 on bass sounds to me like a questionable choice. If this is a project studio kind of thing and the price tag is appropriate for that, OK, but I'd feel justified in pressing for another mic choice. The 421 would be perfectly fine with me, as would any of the other standbys we talked about. None of those mics in the full range "radio booth" dynamic category are expensive or exotic. I'd worry if none of those were available and I was paying real money. My project studio has a selection of those.