There is no station that connects ACE with Bart. Your best bet is to take the ACE Train to Pleasanton and use the Wheels 54 Bus to go to the Dublin/Pleasanton Bart station.
My husband commutes from Manteca to San Jose daily (Berryessa/101). Depending on the time of your commute, the Ace Train may provide you with a more relaxing way to travel. It can be costly so I recommend doing your homework first. http://www.acerail.com
Mountain House is a great community and, in my opinion, its market will bounce back much quicker than its sister cities within San Joaquin County.
I live in Dublin but I am moving to Tracy to be near my family because I have a 4-month old daughter they want to babysit. I take the ACE train currently and will continue to do so once I make the move. I would check on connecting shuttles near the stations and their routes. They will help get you to where you need to go. I take the ACE train from Dublin to the Santa Clara station and it costs $94.50/month. It's $122.50/month if you take it from Tracy to the Santa Clara station. Very affordable. It's actually faster than me sitting in commute. Gas costs me $70 or so every 5-6 days and I just purchased new tires for my car which were $800+. Take the ACE train. You won't regret it.... more