To determine the actual quantity of sand per unit volume of cement in a concrete mix with proportions of 1:3:6 (cement:sand:aggregate), we need to consider the bulking of the sand, which is given as 15%.

1. Understanding the Proportions:
- The proportion 1:3:6 means that for every 1 part of cement, we have 3 parts of sand and 6 parts of aggregate.
- This ratio is based on volume, so if we have 1 cubic meter of cement, we will have 3 cubic meters of sand and 6 cubic meters of aggregate.

2. Accounting for Bulking:
- Bulking refers to the increase in the volume of sand due to the presence of moisture.
- In this case, the bulking of the sand is given as 15%, which means that the volume of sand increases by 15% when it is loose.
- To account for bulking, we need to adjust the volume of sand in the mix.

3. Calculating the Adjusted Volume of Sand:
- Let's assume the volume of cement is 1 cubic meter.
- The volume of sand in the mix will be 3 cubic meters (based on the proportion).
- However, due to bulking, the actual volume of sand will be 3 cubic meters + 15% of 3 cubic meters.
- Calculating, we get:
Actual volume of sand = 3 cubic meters + (15/100) * 3 cubic meters
= 3 cubic meters + 0.45 cubic meters
= 3.45 cubic meters

4. Determining the Quantity of Sand per Unit Volume of Cement:
- Now, we need to find the quantity of sand per unit volume of cement.
- Since the volume of cement is 1 cubic meter, we divide the actual volume of sand by the volume of cement.
- Calculating, we get:
Quantity of sand per unit volume of cement = 3.45 cubic meters / 1 cubic meter
= 3.45

Therefore, the actual quantity of sand per unit volume of cement, accounting for a 15% bulking, is 3.45. Hence, the correct answer is option B.