The basking bulb should replace the CHE. That is for the basking area. The best bulbs I have found to use are halogen, but any incandescent will work. You need to be sure it is an incandescent bulb and not LED or CFL as these will not produce the heat that is needed. I buy my 50 watt halogens from the dollar store, my 75 watt halogens for winter months I get from any hardware store like Home Depot. Amazon has a good selection as well.
Once the light is set up for heat you want to place the probe on the basking area (where the dragon sits) and as close to the middle of the bulb as possible. This should give you the maximum heat output reading.
The CHE can be used in a different area of the viv. Either mid to cool side if needed to bump up temps for times (if and when) the viv is too cool. For instance, mid tank temps not reaching close to 80F and cool tank temps getting below 65F in the evening. Or when the dragon is ill and needs the overall tank heated to give the immune system a boost.
I have attached pics of one of the basking area set ups for my dragon. As you can see the 75 watt spot is the correct distance to achieve a basking area of 100 to 102 F for my adult dragon. The probe is placed on the basking area at the middle of the bulb. Littlefoot, my dragon is sitting on it. The read out is placed on the cool side as the unit reads in and out temps or cool side and basking side with probe.
Different areas, textures, colors and materials will all absorb the heat differently. So you cannot get a good gauge of temp by feel. The tile should feel cool to the touch as it is at the bottom of the viv. Wood may feel warmer as it is closer to the CHE. I personally would not take pet store advice as accurate. Pet stores generally do not always have the best husbandry practices. Even my local reptile shop as good as they are have the reptiles in conditions that are not meant for long term care.
These beardies are daytime desert species. They are active during the day and require mimicked sunlight...light and UVB to thrive. Although your dragon is using his basking area with a CHE it is because it is warm and he will use that area for warmth, but he also needs the light.