Hi Anaphase,
I used to live in Arlington and used the bike path from there to commute to Harvard Square and now my boyfriend lives in Bedford, now I ride it to work occasionally (MGH/Charles Street) and from Brookline. Let me see if I can succinctly give tips.

I can't comment on Lowell to Bedford. But the ride from Bedford using the Minuteman trail to Mass Ave, Mass Ave to Porter Square, Somerville Ave-Beacon/Hampshire/Inman/Kendall Square, to Charles St. is about 18 miles one way. The ride from Bedford to Arlington Center at 7am is pleasantly empty. In fact I feel like I'm going the wrong way: lots of riders heading out for early morning group rides. Sigh.

Anyway, at A. Center, cross Mass Ave and pick up trail at Carberry's bakery (and pick up a pastry if they are open. Try the Hekla with frosting) The trail from here to Alewife is busier with morning walkers and foot commuters.

At Alewife, take left on road at end of path, ride with cars and take right onto path marked by huge stones (just before underpass). Pass the playground, stay left under road. Pass other T entrance. Stay left around football field. Cross deadend road. Ride path to end at Mass Ave.

From here ride into Porter, left on Somerville, right then left to stay on Beacon. Shoot down thru Inman to Kendall. From there, don't know how to suggest to get to Galleria, but I'd sneak over on 1st or 2nd street.

Keep in mind the bit from Mass Ave on, means comfort with cars, car door watching, and taking left turns. It does get easier over time. And "bike lanes" are officially marked on this bit of the route, but sometimes it just means a line with a bike symbol.

The path in the evening tends to open up (less people) once you get out of Lexington. I find it to be a nice winddown after work, and commuting through Cambridge.

Good luck! Let me know how it goes.