Most public transport in that area would be by bus, and there’s few options. I believe bus route 354 begins in Burlington and passes through Woburn going towards Medford, where it becomes express and goes straight into Boston, dropping off at State St. I believe it also only runs on weekdays but someone could correct me on that.

Woburn has a stop on the commuter rail at Anderson/Woburn station. It’ll get you into North Station in about 25-30 mins, but unlike other commuter rail stops in cities around the area, it’s not located in the “center”, but a bit far out, so you’d probably need a bus to get there unless you live within walking distance.

In general, public transport in these towns is lacking and the options are not necessarily fast.

Edit to add: Burlington also has the 350 bus that will bring you to Alewife in Cambridge to connect to the red line.