Depending where you are (I'm in the UK), many universities offer various conversion courses - postgraduate certificates or even Master's degrees - into computing for graduates in other subjects. These typically last for one full year and may be fairly intensive, covering core computer science topics only, but many of them offer the option of completing a Master's dissertation to get an MSc, which could give you a chance to get practical experience while gaining your qualification e.g. by working on a project in collaboration with a local company.
As many people in the industry will tell you, you don't need a CS degree to do well, especially if you have a strong numerate background as you do, and many of us came into the industry from all kinds of backgrounds (my first degree was in German Language and Literature, and I got a job as a trainee programmer having done one year of CS as a minor subject at university). However, in recent years it has become much more difficult to break into the industry without a relevant degree (at least here in the UK), or even with a degree - one in six CS/IT graduates in the UK can't find jobs - and there are also a lot of equally inexperienced but very cheap CS graduates from low-wage countries in the industry here, which increases pressure on recruiters to exclude "unqualified" candidates and depresses wages. The market where you are may be very different, of course - let's hope so!
On the other hand, if you have been working professionally in another role for a while, then you should have a lot more to offer than a fresh graduate, so you might well be able to leverage your work experience to break into software development e.g. in a company that could use your non-IT skills. Have you explored the possibility of moving into development with your current employer? Many businesses complain that even if they can find people with technical skills, those people lack business skills or specialist understanding of the relevant industry, so somebody who can both code and understand the business would be very valuable.
You should probably start networking to build up contacts with potential employers or professional colleagues in the software industry in your area e.g. join relevant user groups or professional organisations, attend public talks or conferences etc. This will expose you to current ideas and practices in the industry, and may also let you in on the informal recruitment network where somebody says to a colleague over a beer "Hey, we're looking for a new junior developer, do you know anybody?". Also keep an eye on the tech websites etc to find out what's "cool" and get an idea of what the Next Big Thing might be - I find lots of interesting stuff at
InfoQ, for example - and of course make sure you check in here at JavaRanch regularly, especially if you need to ask questions (or indeed can answer other people's questions)!
Have you done much coding? Definitely try to get lots of hands-on practice at coding, preferably with the help of a good teacher (i.e. somebody who knows how to code well and preferably how to teach as well), or from a good book or an online course. It's easy to learn bad habits when you're starting out, and it can take a long time to break those habits afterwards! Many people suggest Python as a good language to start with, as it's a pretty clean object-oriented language, so the OO practice will help you with Java, but Python is easier to pick up than Java and has a lot of powerful and sophisticated libraries, including lots of support for maths and science applications. It's taught in the early stages of many CS degrees, and is used by big players in the industry such as Google.
If you want to learn Python, there are some free courses at Coursera (see below), but I recently took the first two courses in
O'Reilly School Of Technology's Python Programming Certificate, which is not free (although it's not too expensive either) and provides you with a dedicated tutor who marks your assignments and gives you feedback, answers questions etc. I had an excellent tutor, and I enjoyed the courses which covered the material very thoroughly, so I can highly recommend these courses if you think this approach might be suitable for you. They also offer Java courses, but I don't know if these are any good.
JavaScript is another option, as it seems to be expanding beyond the traditional browser environment into new areas quite rapidly e.g. on the server, or as a database query language in NoSQL DBs, etc. It's easy to code badly in JS, but the language is very powerful if you know how to use it properly. I don't know much JavaScript myself, but we have a very helpful
resident JavaScript Ninja here on JavaRanch who can provide lots more advice on JavaScript if you need it.
Finally, I can also recommend Coursera's courses on computer science - they're free, well-structured and give you a focus for your own learning. I'm just getting to the end of the
Programming Languages module, which is an excellent course taken from the undergraduate CS degree at the University of Washington, very challenging but also very rewarding and well taught. There are
a lot of CS courses starting in the next few weeks, so why not sign up for one and start your learning process now? Another option is
Udacity, which has fewer courses but they look very good as well, and some of them are more flexible than Coursera, allowing you to study at your own pace.
Good luck!
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