I know you want to work on having your boy play independently, but that means buying into the assumption that he needs to play on his own a lot (or be willing to go into a bouncy house at 2). I will get to the crux of your question, but first I want to get this one out of the way. In regard to things like the bouncy castle and parties, He is two. He has only recently mastered walking, and most children at this age still can't really jump (it is around 3 that MOST kids learn this skill - still a few months off). Even if he can jump, he probably has not mastered it yet, and landing or taking off from an uneven and moving surface is entirely different to jumping from a still and relatively flat surface. Think about how scary a bouncy house would be without a hand to hold if you were in there with a bunch of noisy kids twice your height with a broken leg and no crutches or hands to hold (balance wise, that is about how it is for him at 2 1/2). Bouncy houses are fun for the late preschool and elementary set - not the two-somethings.
At a party being unwilling to leave your side, doesn't seem to me to be the same thing as lacking the ability to play independently OR being unwilling to participate in groups (from your question it seems he does fine at preschool or nursery). So this aspect of your question really does seem like a different question to me. For that reason, I will address what I interpret as your main question which is "How do I get my other stuff done when our boy won't play independently?"
Your son is two and he, developmentally isn't really supposed to want a lot of independent time yet. That doesn't mean however, that you can't still get your stuff done. PLUS by offering and allowing him time WITH you now, he is likely to be more independent in a healthy way sooner than without the time and attention now anyway. Given this, I thought I'd offer some alternative ideas for you in dealing with your situation that can still meet both your needs and his.
The alternative is to involve your son in what it is you are doing. Some examples:
If you are folding laundry hand him some washcloths and let him try his hand at folding. Yes you will need to go back and refold, but in the meantime he is learning that you value your time with him AND that you value his contribution (a REALLY important lesson that helps with a lot of things later on - including discipline and the development of the confidence required to be an independent young man). Laundry also makes for good "matching" lessons and opportunities when it comes to pairing socks. Also importantly, he is learning social skills as you speak together. While you talk about things that are NOT toys and games, he is learning about how to learn, how to listen and the give and take of language.
In the kitchen, give him something to stir or mash or knead (great life skills to know and sensory experiences). It is a good sensory experience for him, he learns kitchen skills from watching you and the two of you can talk about what you are doing which also helps him build his vocabulary. You could also put a little water in the sink and let him "help to wash dishes" as you make them (just don't have any knives wind up in his reach). Dish washing is another experience that teaches him a life skill AND gives him another important sensory experience.
This may sound weird, but seeing others use the toilet is a part of him becoming potty trained. Let him join you. As long as he sits a little away and gives you some space and isn't trying to play in the toilet, tub or trash, he'll be safe and you can talk to him about how potty goes, well, into the potty while you are at it.
I think you probably get the idea. If, he would rather play - let him and then he is getting practice playing on his own, by his choice at his comfort level. He may be perfectly comfortable playing independently as long as you are in the room. If he is, give him plenty of this time. You can do work (including a lot of housework and office work), read or just enjoy watching him during these time periods. Even phone calls will work fine too. The more you just accept the idea of time spent together now, the more he'll learn and sooner than you'd really like he'll become the more independent person you are wishing for now.
On the occasion that you really do need to have a minute or two to yourself, Morah Hochman has the right idea in regard to suggesting that you tell him exactly where you will be, why and for approximately how long and then give him something to do while you are away, "I will be right back, how about you make superman fly over the tower of blocks (or whatever you are playing) while I am gone and then we will see what he does next." Just make these absences SUPER SHORT.
Hope this helps.