Congratulations on all of your success so far and your decision to consider furthering your education. I'm in a very similar position as you and I'm currently considering distance education for a Master's degree in Computer Science or Software Engineering. I'll do my best to answer your questions the best that I can.
1) The difficulty of getting into programs varies, but I would say it's probably easier to be admitted into an online program than the live/in-person program. I was accepted into all programs that I applied to. (I graduated with a science degree at the top of my class, have good test scores and work experience, so I'd say I'm a strong candidate for most programs.) Just be careful about some "diploma mills". Some schools are "for profit" and let everyone in. Just try to find an established school that has a distance education component and you should be in good shape.
2) Whether you go straight to a Master's degree or not depends on you and your life situation. You can consider your situation from a few angles.
Job Opportunities/ Return on Investment: I think that most computer related careers are available to people with a technically-oriented bachelor's degree so the return on your investment might be neglible since you already have a bachelor's. You mentioned that your employer may pay for it, so your investment might just be your time and energy.
Timing and Other Life Events: If you are willing and able to invest 20-40 hours per week for the next 2 years or so, then getting a Master's could be a good idea. If you're planning on having a family in the next few years, maybe it's a good time to get this done. If you're just starting a family or have other commitments, then maybe you should wait. Graduate schools aren't going anywhere.
Certainty: How certain are you that this is the career/industry for you? Do you have significant experience working in software engineering? I just ask because you may find that this is not what you actually want to do, especially if you've never done it before. I've changed my mind a lot in the past. Since I've graduated a few years ago, I've worked in sales, health services, teaching, insurance, and web development. I always thought I was going to enjoy those fields until I actually worked in them. Once I started doing web development and LOVING it, I decided it's worth pursuing an education to take me a step further.
3) There are a lot of programs to consider. I started by looking at US News to see a list of highly-regarded schools. I then visited their websites to see if they had distance programs in Computer Science. Another few schools that I've considered are:
- Brandeis University - Master's in Software Engineering
- University of Bridgeport (CT) - Master's in CS with Software Engineering Concentration (ranked in top 10 online CS programs nationally)
- Harvard Univerisity - they have an Extension School where you can get a Master's in Liberal Arts with a concentration in Software Engineering
You should also consider the finances and "pacing" of programs. Some programs are really expensive. Also, some degrees are accelerated and take 18 months, while some programs take 3-4 years to complete.
Sorry for the long response. I just wanted to give you the information I've been researching this for several months. I wish you the best of luck with everything.