A thermocouple produces a voltage proportional to the temperature of the junction. In this respect, a thermocouple response is instantaneous. However, a T/C is not usually used to measure itself, its used to measure an object or environment. In order to accurately measure the temperature of an object/environment there needs to be sufficient time for the thermocouple junction to reach the same temperature as the object. Anything that slows down how fast the T/C junction temperature equalizes with the object temperature slows down the T/C response time. This includes sheathing, insulation, thermowells, etc. For fastest response, a very thin bare metal T/C bead attached directly to the object is desirable, but there are many other factors to consider besides fastest response. A thin bare bead is subject to mechanical and chemical damage. Sometimes the bead must be ungrounded and cannot be in direct electrical contact with the object being measured. You need to consider all those factors when choosing a T/C style.
You can buy T/Cs that have an exposed bead, or you can make your own out of the appropriate thermocouple wire. Most commercially produced thermocouples have a welded bead. You can also purchase your own T/C welder. You can also make your own by twisting the wires together and mechanically securing them. Even placing the two wires together under the same screw will work. If you are 100% positive that the object being measured is at a uniform temperature and the object can conduct electricity you don't even have to have the wires in physical contact, eg, one wire could connect to one end of a steel bar and the other wire to the other end, and as long as the steel bar is of uniform temperature you can accurately measure the bar's temperature.
With a little more info on your application you could get some good advice from the forum members.
