You don't receive a bonus at all unless you have a smartlink system
Having done a good bit of research on this subject to try and conclusively answer a similar question of my own I have to conclude that without any equipment or augments a Technomancer is completely incapable of receiving any bonuses from a smartgun system, including the increased accuracy.
It's not a question of whether you're 'wired in'
The wireless bonus of a smartlink system is provided when your smartgun is permitted wireless access to the Matrix.
SR5 Core Rulebook, Page 421:
When an item has additonal functionality when connected to the Matrix, it's described under the "Wireless" entry in the item's description. This functionality only applies when the device has access to the Matrix, which is most of the time unless your gamemaster says otherwise, like if you've entered a wireless static zone. If there is a Noise rating from a situation that is greater than the item's Device Rating, not including distance, the item temporarily loses its wireless functionality (see Noise, p.230). These benefits only apply when the item's wireless mode is on. Your Ares Alpha can't auto-adjust for the wind direction and speed if it can't download local up-to-the-second weather conditions [...]
The Technomancer rules also have this to say about your abilities in the "Living Persona" section.
SR5 Core Rulebook, page 251:
You are not a device, so you cannot be a slave or master, nor can you be part of a PAN or WAN.
This implies you can't connect directly to a device through resonance abilities in the same way that the devices in someone's PAN are connected. Yes, a smartgun is downloading data from the Matrix while it's in wireless mode, but the targeting data your smartgun computes from it isn't uploaded back to the Matrix and can only be accessed/interpreted through a direct connection to a corresponding smartlink system.
SR5 Core Rulebook, Page 444:
Smartlink: [...] Without a smartlink a smartgun system just sends out data that isn't received by anyone and has no effect. A smartlink installed in a natural eye or in a pair of cybereyes is more effective than a smartlink installed in an external device.
SR5 Core Rulebook, Page 433:
Smartgun system: [...] The smartgun features are accessed either by universal access port cable to an imaging device (like glasses, goggles or a datajack for someone with cybereyes) or by a wireless connection working in concert with direct neural interface.
Long story short, if you want to use a smartgun at all be prepared to strap on some smartlink-equipped goggles/glasses for your accuracy and +1 dice pool bonus, or pay up the essence to get a smartlink system in your eyes and some method of connecting it to your gun (Datajack, Implanted Commlink or similar) to get the full +2.