I've seen a lot of tips about cutting the first coat of polyurethane with mineral spirits to reduce drying time. However, given that it's the first coat, I have a full can of polyurethane. I'd pour some polyurethane out into a separate container, but am worried this will create air bubbles. Likewise, I imagine the act of adding mineral spirits to polyurethane could also introduce air bubbles.
I add 20% thinner to my polyurethane to promote even coats, prevent bubbles(they pop more easily on their own when thin), and speed up drying time. You can alternatively use lacquer thinner and this will dry even more quickly due to it's lower flash point -- but in high temperatures it might dry too quickly.
As far as methodology for mixing, I have a "mixing can" that I bought at a big box store -- they sell empty paint cans -- and I add 20% thinner and the rest poly. I use a plastic can attachment that acts as a spout to prevent poly from filling the lid gap when pouring. Stir with a stir stick. I don't get too many bubbles but I don't worry about them either because they pop on their own. Pour onto the side of the can to prevent bubbles (think of pouring beer from a bottle into a glass).
I normally would not recommend thinning urethane. If you have a new can of fresh urethane, it should be ready to go. I would try to apply it thin rather than a thicker coat. If you feel you really need to thin it, just slowly pour some in another container and add a small amount of thinner at a time. Stir it slowly and you will have no issues with air bubbles. Never shake or use a high speed mechanical mixer. If you see some small bubbles, don't worry. They should dissipate during application. the only time air bubbles are an issue is when the product is shaken hard and the urethane appears real cloudy.
If I may add something here: they sell polyurethane that is pre-thinned. One brand I've used is Min-wax Wipe-On Poly. It's intended to me wiped on with a rag and I've never had any issue with bubbles.
This is actually all I use any more. I have not examined the cost though; it could be that this product costs more than simply buying poly along with a can of thinner.