You have several 'translations' that need to happen in order to achieve this.
First - your Bose system runs line level, balanced. Your phone as it stands needs mic level, unbalanced.
Unbalanced is 'regular home audio' - 2 wires, one signal (hot) the other ground [people tend to think of them as positive (+ve) & negative (-ve), but that's not truly the case.]
Balanced line is used in pro audio equipment to be able to push signals much, much further without introducing interference noise. It does this by using 3 wires instead of 2. Instead of just signal & ground, it has +ve signal (hot), -ve signal (cold) [which is exactly the same as +ve but phase reversed] & ground.
Rushing quickly past the maths, if you get interference on a cable, then by phase-inverting -ve & adding it to +ve, you cancel out the interference. [Don't worry about exactly how.]
To unbalance your signal, you need to connect the cold to the ground & send that to the ground pin at the other end. Hot goes to hot +ve. This cancels out the phase reversed signal so your receiving end can understand it… otherwise they'd add up to silence.
So, to get round your first issue, you need to find an unbalancing cable, or make one up.
Regular TRS to TS jacks you find on eBay & Amazon will connect the wrong pins, so you'll do best to find a local pro music store & ask them to get one made. You want TRS balanced to TS unbalanced. They'll know how to do it properly.
Secondly - & this is going to need hardware - you need to match your levels properly. Audio levels are measure in decibels (dB) [but there are 20 ways to measure dB, so again I'll skip the math]. There's a comprehensive, if somewhat mind-numbing, guide here - BiAmp.com - Gain structure: input and output levels
For our case we're going to be working in dBu which goes from -infinity up to zero & then past into positive values. Mic level is around -60 up to -35dBu [that's very quiet] Line level is -10 on consumer gear but +4dBu on pro gear [that's really loud.] Every 3dB change is equal to double the power, every 6dB is double the volume, so you see it ramps up a long way. These are nominal levels, not absolute.
Your phone's input is expecting mic level. Your Bose is outputting pro-level line.
From your S1 resource -
¼ inch (6.3 mm) Tip-Ring-Sleeve jack: Nominal +2.4 dBu, Max +20 dBu
Using a Tip-Sleeve unbalanced cable will result in a drop in the audio level of -6dBu.
There is no limiter on this output so you may get more than the rated maximum, but it could sound distorted.
That's a whole lot of level for a mic input - possibly enough to destroy the circuit.
You can get consumer line-mic level adapters pretty cheap. This one from Headset Buddy for instance. However, they expect consumer line level at -10, not pro level at +4. They provide a -20dB reduction… this is nowhere near enough.
To be safe, we need to figure out how many volts this all translates to.
The calculation is more than I have fingers & toes, so this handy calculator comes in… err… handy - http://www.sengpielaudio.com/calculator-db-volt.htm
From the S1 guide above, we need to be safe to +14dBu after unbalancing. Using our handy calculator, that comes out to 3.88Vpp [that's volts, peak to peak… don't worry about it].
The only product I can find that will take that kind of level straight into an iPhone is the IK Multimedia iRig Pro I/O at about £$€150. This can handle from 30 mVpp to 6.9 Vpp on a combination line/instrument preamp, so should have plenty of headroom.
Armed with that & your unbalanced cable - you're ready to go ;)