If you already have a bachelor and familiar with team-based projects working towards concrete deliverables, the step towards an ID job will be much smaller than if you started from scratch. The main thing about product designers is that they deliver production plans, and on the way have to impress clients and prove that the concept will work from a business, technical, aesthetic and human-centered viewpoint. So of course you can do your own research to develop yourself. However if you have a great university environment and actual clients that will greatly help. So if you can enroll into the open classes that is wonderful. Keep an eye on local design-related events too and if you post work to these forums you have a chance to get very valuable feedback from top designers. An alternative route for a low budget is to start your career in related fields like graphic or interior design, for which you can enroll in courses from private companies, at least in Europe you can.