From Astoria, I think your quickest route would be by car, otherwise, you'll be heading into manhattan and heading uptown on a combination of busses and trains. Looking up the location on the map, I've taken the m60 to the 4 and made it to the Yankee stadium stop in about 35 minutes when I catch the connections right, you'll have a little walk from Yankee Stadium, but my commute via train to midtown is 40 minutes on average, so I don't think that the m60 to the 4 would be the worst commute ever.
That said, I went over the triboro (or RFK) bridge to the GWB twice last week and I was into the Bronx in about 30 minutes both times from 44th St. Based on Google Maps, you're close to the Major Deegan, which connects directly to the Triboro, so overall your commute out shouldn't be that bad. Coming back, I can't really speak to, as I was coming back in the early afternoon, but I'd assume that the traffic is heavier in the evening.
I'm sure that someone here can speak to living in the bronx, and there are lots of parking complaints, but hopefully this helps.