I would like to glue twine to a wine bottle and convert it into a lamp/light. Is there a recommended adhesive that will work for this purpose while being safe from the radiant heat of the bulb?
The amount of heat generated by an incandescent light bulb in an enclosure is not particularly great relative to many adhesive types. One can purchase a silicone product known as high temperature RTV (room temperature vulcanizing) which can tolerate temperatures sufficiently high to ignite paper. It's not particularly suited to your project, however, as it is often bright red and would be unsightly if any oozed from between the runs of twine.
Many epoxies are capable of tolerating high temperatures, especially as they can generate uncomfortable levels during curing. If you scuff up the surface of the bottle with coarse sandpaper prior to applying epoxy, the adhesive will adhere well and provide that much more strength.
A local hobby shop will carry various types of epoxy. The faster curing versions, frequently called "five minute epoxy" will harden quickly but be weaker than the fifteen minute or thirty minute version. The longer cure types will also tolerate the higher temperatures better.
I've used the 30 minute cure version frequently. It has to be applied when temperatures are at 70°F or above. Some hobbyists also use a heat lamp or incandescent bulb to speed up curing. Heat guns are used, but with temperatures above 450°F from such a device, one risks burning.