DP is fine, you're adults, he's not a boy, so BF sounds daft! I call my DP that on here as I feel like a twat calling him my BF. Yes you could refer to him as 'the man I've been seeing for 4 months' but wtf is the point of abbreviations if we're not allowed to use them!
Anyway, to the subject in hand, I also introduced my DP to the DCs quite quickly according to MN 'rules' as I thought it was important to find out if they all got on ok. It happened spontaneously, as you have tried to do here, and it felt natural and not forced in any way, not some big "oooh you're going to meet someone very special" - just "we're going to the cinema, do you want to come along?"
If I had become very attached to DP and then our kids had met and hated us or each other, it would have been a deal breaker. Not much point in investing a year in a relationship, only to have to finish it because the other important people in your lives don't get on.
Compatibility issues are the main reason step-families break up, so what's the point in waiting until the two of you are certain about your future together, only to find that it's not going to be as simple as that if your DCs hate him?!
How long you've been dating isn't as important to DCs as how comfortable they are with the situation.
Whenever you're ALL ready is the right time. Unfortunately it seems that for DP this may not be now, but that doesn't mean you have to wait for a marriage proposal before your DCs can meet him.
They are aware that you're dating, they will be curious to know with whom.
FWIW, my ex has been dating someone for a few months. He told the DCs about her and then they met her within a week. To them, it was as new a relationship as if he'd only just met her because they had only just found out about her when they met her IYSWIM. I'm not saying this is wrong, just that to the DCs it didn't really matter how established the RL was.
If they subsequently split up, my DCs won't really be that traumatised by the whole thing, as they haven't really invested any time thinking about the future with this lady around. They like her and they're happy for their dad, but they haven't really bonded with her yet as they don't see her very often.
Whereas if my DP and I separate the DCs will be gutted because we've been together for a couple of years, our families are intertwined and they spend a lot of time with my DP. Time is not a guarantee that the DCs won't get hurt.