I don’t understand the question
if you are speaking of a formal Holy Hour with exposition of the Blessed Sacrament and Benediction, the priest has to be there. I have never been in a parish that does have regular times for exposition and adoration where the priest does not participate. \
If you mean you have a chapel where the blessed Sacrament is exposed for adoration by the faithful for a certain number of hours, either the priest or deacon can expose and repose. No priests do not customarily have a tabernacle in their bedroom, although if they live in a convent or monastery the house may have a chapel of reservation, where even Mass may be celebrated. Most priests I imagine simply spend part of their prayer time in front of the Blessed Sacrament in the church or chapel of the parish where they serve. And yes, they might prefer part of their prayer time to be private, so you might not know about it, and why should you?