Lots to consider here. "Free-flight" model airplanes and gliders fly without any control inputs from a pilot whatsoever (and no automatic electronic stabilization systems either). One branch of this is called "towline gliders" and the "pilot" runs along pulling on a line attached to the glider to get the glider into the air. The line is attached to a tow hook just forward of the CG of the glider.
If you really want to dive into the subject, you could try to find out just exactly where the tow hook is in relation to the CG for various towline free-flight model gliders.
In full-scale sailplanes, the best location for the tow hook is near the nose for a greater tendency to track straight (and not pitch up) during aerotow, and on the belly near the CG for maximum altitude gain during a winch launch or car tow launch, both of which involve a tow line running to the ground. Some sailplanes have only one tow hook, rather near the CG, though this is not optimum for tracking straight during aerotow. Reasons for omitting the nose hook include-- leaving the nose free for something else like a pitot tube, keeping things simpler if there is already a hook near the CG, and keeping things more streamlined (often the hook near the CG is mounted on the landing gear assembly, and retracts with the wheel.)
It is certainly possible to do an car tow launch with a sailplane using just the hook near the nose, but the pilot typically exerts a lot of aft pressure on the control stick, often sometimes getting the elevator into the full up position to allow the glider to really climb steeply despite the downward pull on the nose. The maximum height gained is always less than on a similar glider with a tow hook near the CG.
It looks like your glider has very modest dihedral (especially in relation to the size of the vertical fin)1 and thus very modest inherent roll stability. It's doubtful that it could be successfully treated like a purpose-designed free-flight towline glider, in terms of tow hook position. If you want it to just follow along behind you as you ride a bike, you need to do everything you can to tip the odds in your favor, as far as preventing the glider from turning away and entering a "lockout" (imagine a kite veering "off course", away from pointing straight into the wind, and diving into the ground with string still tight.) The string should connect rather near the nose-- perhaps 1/3 of the way between the tip of the nose and the CG. Start there, and then start moving it slowly back to see if you can get the glider to progressively climb a bit higher each time, without going out of control.
Re your idea of connecting the line to both wings-- what about a three-point connection that includes a point maybe about one third or one half of the way out along each wing, and also includes a point on the fuselage closer to the nose? With the three lines converging several feet below the glider? It seems that this would "lock" the glider in to a level bank attitude, at least once the glider has gained some altitude, and so long as the glider is staying directly behind the bike. But it seems that nothing would stop the glider from rotating (yawing) around the towline as it veers off course-- like the "lockout" dynamic we see with a kite on a string, as noted above-- unless the net effect of the three lines is to cause the tow force to converge to a point well ahead of the glider's CG. It looks like your best bet is going to be to get the tow force to act rather near the nose, in which case the additional lines to the wing are only going to be a hinderance. You'll likely have better luck trying to just fly it like a glider (i.e. with a single towline), rather than treating it as sort of a hybrid between a glider and a kite.
The Blanik L-13 glider did indeed use a 2-point v-bridle for winch launching and car towing, but the bridle was connected to one point on each side of the fuselage, not on the wings. See page 7 of this manual for a very brief mention-- note the reference to "very light" control forces, which would have been in reference to pitch control.
Presumably the reason for this design was to get the points of connection absolutely as close to the CG of the glider as possible in the fore-and-aft sense, for maximum altitude gain during car tow and winch launching. It would not have been possible to put a tow hook on the belly of the glider in the same fore-and-aft location, because it would have been behind the wheel. Most other sailplanes with a tow hook on the belly of the glider near the CG have it positioned just in front of the wheel.
Please let us know via a comment or an addendum to the question, or a self-answer, what you actually find to work best!
- Some free-flight model aircraft actually have rather modest dihedral, but they invariably have very small vertical fins. A large vertical fin actually works again inherent roll stability, by minimizing sideslip as the glider is rolling or turning. The interaction between sideslip and dihedral is key to roll stability dynamics.