No, you do not need the Bishop’s permission to bless the Sacrament outside of church.
If you are going to represent the Ward in blessing and passing the Sacrament to a Ward member or members, the LDS Church requires that you get permission from the Bishop.
If you are visiting family or a friend, you don’t need permission from the Bishop at all, if you are a worthy holder of the Priesthood according to the scriptures (D&C 50:34). The Bishop has no jurisdiction beyond what people give him by common consent (D&C 26:2). Anything that LDS leaders claim otherwise is an example of unrighteous dominion, because it represents a prideful claim to a domain they have not been given authority over (D&C 121:39). Those who request the ordinance without any reference to the Bishop have not given him consent to preside over their individual request, and the Lord has not stifled all Priesthood use within the confines of church jurisdiction, either. You can use the Priesthood outside of church according to God’s will, but within the Church everything is governed by the consent of those within that group.
It is false to assume that the Bishop has control over everything within the Ward boundaries. He only has consent from those who are members who apply to the Bishop for member benefits, including member-based Sacrament services. Members can and do request Priesthood benefits outside of their role as members, which also includes the Sacrament and baptism, etc.
Don’t give up your liberties as a Priesthood holder. Give unto the Bishop the things that are the Bishop’s, but also give unto God the things that are God’s (see Mark 12:17).
If someone asks you to perform an ordinance, and doesn’t refer to their Bishop for permission, pray and get permission from the Lord and proceed (2 Nephi 32:9).
If they ask you to perform an ordinance as a representative of the Ward, explain to them the difference and only proceed if they understand you are using your Priesthood independently as a representative of God. God can and does recognize righteous Priesthood use outside of church jurisdiction. If he didn’t, then Joseph and Oliver’s baptisms would be invalid and John the Beloved would also be condemned (JS-History 1:68-75, D&C 7).
If you perform the Sacrament outside of church jurisdiction, be sure to take advantage of the opportunity to do it more accurately with wine (or grape juice if you have a medical reason not to drink alcohol), because the Lord said in scripture, “For, behold, I say unto you, that it mattereth not what ye shall eat or what ye shall drink when ye partake of the sacrament, if it so be that ye do it with an eye single to my glory—remembering unto the Father my body which was laid down for you, and my blood which was shed for the remission of your sins” (D&C 27:2). Therefore, the LDS Church cannot restrict you from using wine to better remember the blood of Christ and the transforming effect that the Atonement has on our lives. Additionally, wine is prescribed for sacraments in the Word of Wisdom and you can still answer that question truthfully when asked in temple recommend interviews (D&C 89:5).
The time has come that Family Home Evenings and other family activities should be more authoritative and full of Priesthood power than LDS Ward meetings (see https://www.lds.org/general-conference/2010/04/the-power-of-the-priesthood?lang=eng). This should include Sacrament and baptisms as well.