Firstly, think of me as a devil's advocate here... I'm simply trying to read the rules and ask why not? and it's answer why? And raise the kind of scrutiny your GM may.
Did you consider using the one new bike in Arsenal?
Thundercloud Contrail: body6, special: +4 mod slots, w/ sidecar that's up to 13.
Using that w/ the sidecar would get you up to 13 mod slots on a bike which is an awful lot.
I don't think anyone would have any issues with making the sidecar the 'rigger cocoon'. Though I'd be a little leary of someone putting it on the bike itself due to common sense... where are you going to put a fully enclosed rigger cocoon on a bike? In fact, that's not a bad idea putting it in the sidecar as you could detach the sidecar then use the bike as a full-fledged combat drone. Given your other comment where are going to put both the cocoon and a 360degree weapons turret?!
Also by your post, your big problem is that you're trying to hide a 360degree weapon turret the big enough to hide a LMG inside of a motorcycle (internal visibility). Use some common sense... of course most bikes aren't going to have space for something that big. Why would an internal forward flexible (front 90degree arc, limited turret), or fixed forward (point the bike at the target to shoot), not be an option? Limiting the traverse of the weapon mount brings the size down 4mods instead of 6.
Just to do this as an exercise.... is this what you're trying to do?
Thundercloud Contrail:
Body: 6(+4modspace), Armor4, Accel 20/40, speed 180, Pilot1, Sensor1
Rigger Adaptation: 1 (you can debate whether this is necessary or not... IMO the books aren't clear.. if the bike has MCO:manual control is it like the '67 chevy and needs the upgrade, or is the manual control an option you get by turning off the built in vehicle drive computer, as it's pretty obvious to me that off-the-shelf motorcycles can't drive themselves lacking the following mod). Cycle only has a Pilot rating of *1*... I'd say this upgrade would raise it to *3* (see the chart on p. 213-214... 1 is dumb as an appliance a drone has a pilot rating of 3).
Motorcycle Gyro: 1, allows operation of the cycle as a standalone drone w/o the sidecar, also necessary for the rigger modification I'd think... in any case handling +2!
Weapon Mount: 6 total, 1 +2(concealed vis), +3(turret flexibility)
Description: the turret pops up out of the motorcycles seat area... obviously not usable if there's a passenger there or as a way to eject someone you don't like

. Also as a GM given the small size of a motorcycle... probably limit the size to a SMG (where are you going to hide something the size of a LMG + ammo inside a motorcycle?)
That still leaves 1 mod free on the bike itself... engine upgrade, armor upgrade, 3 if you limit the traversal of the turret to forward only. Armor upgrade would help a lot if you're going to use it as a combat drone (only 4 base armor... could be raised to 12armor for 1mod point). If you get rid of the 360 traverse turret, you could still guard your back with something like a 'road strip ejector' for 1 mod.
Sidecar: 1, sidecar drawbacks to speed/accel
In the sidecar, Rigger Cocoon: 1mod
2 more mod spaces free for the sidecar... since this is a rigger and the rigger is blind in his cocoon I'd probably look at putting upgraded sensors on the sidecar itself, or a minidrone rack or two.
Remember: being able to launch a small or two mini-micro drones increases your mod slots because each of those drones has mod slots... EG: rather than putting ECM on the bike itself... you could put it on a small flying drone. So that's a way to put loading options on the bike after the fact. But in a chase type scene... the small drone probably won't be able to keep up... so while it does magnify your slots there are some drawbacks and costs.