Tip #1: Names
If you're in a public vanilla setting, and you address your dominant as "Master/Sir/Mistress/Daddy/Mommy/Owner/Domly-Dom-Of-All-Doms/Etc," and he/she answers you as "Pet/Sub/Slave/Slut/Minion-To-Do-My-Bidding/Etc," you may get some funny looks from those who overhear you. The significance of these titles is more than the word you use, it is usually a sign of respect and acknowledgement of their power/dominance over their submissive, therefore, if you change the word, the meaning should not be lost. It may be wise to come up with a more subtle title to use in public settings where "Master/Mistress/Etc" may not be appropriate. What you choose should ultimately be negotiated by those involved, but here are a few ideas: "My Love," "Darling," "Honey," "Princess," "Kitten," and "Baby." Pretty much any name will do, as long as it can be used in the same context as their usual title. To vanilla ears, "My Love, is it okay if I order desert?" sounds a lot better than "Master, may your slut please have desert?"
Tip #2: Symbols Of Ownership
In many BDSM relationships, there is usually a symbol of ownership. The most common sign of ownership being a collar. Some collars can be more discreet than others, such as an eternity collar, which is a simple metal band that locks in the back via a tiny screw. But in many cases, they are composed of leather or other material, with either an O-ring or other design and a buckle in the back. The latter is probably the most common type of collar I've seen, and the style of my own.
Unfortunately, wearing a bright pink leather collar with a huge O-ring on the front can draw quite a bit of negative attention, as it is not very discreet and is somewhat obvious about what it is used for. Luckily for me, I live in a very punk-esque area, and my collar can usually pass as a necklace if I am dressed kind of punk-ish; however, if I happen to be in a more conservative setting, such as at church with my Master, I am sometimes bombarded with questions and accusations due to my collar drawing so much attention. Personally, if I am asked in those situations, I choose to tell a censored version of the truth, and simply say it was a gift from my fiance and leave it at that. But if you wish to be more discreet, there are a few options.
First, you could purchase an eternity or gorean collar which, as I described before, are usually thin metal bands that lock discreetly in the back; however, they are somewhat expensive, and traditionally, an eternity collar is a huge commitment in a d/s relationship, similar to a wedding ring if you want to draw a parallel between the kink and vanilla worlds. Next, there are slave bracelets and anklets, which, like an eternity collar, are usually thin locking metal bands, but they are worn on either the wrists or ankles as opposed to the neck, and may be hidden more easily. Alternatively, you could choose to replace your usual collar with another piece of jewelry. I have seen some couples replace a collar with a necklace given to them by their master for more conservative areas/events; in these cases, the symbolism of the jewelry stays as a sign of ownership, and it is only the physical symbol that changes.
Tip #3: Seating
In many d/s relationships, there is a pre-negotiated protocol for seating, usually involving the submissive kneeling at the dominant's feet. Unfortunately, in most situations, this can not always be an appropriate thing to do in public. If a submissive were to kneel at a dominant's feet under the table at Olive Garden and be fed from the dominant's hand, it's obvious to say that they would get quite a few strange, or even mean, looks from passers by. Luckily, there are some more subtle forms of seating that actually can be seen as acceptable in society and still have a feeling of dominance and submission.
For example, instead of the submissive kneeling on the floor, a more subtle approach may be to negotiate that the submissive must be seated lower than the dominant in public. This would work particularly well in a home setting, where the dominant could sit on a couch, and the submissive could sit on a pillow and lean her back against his legs; this still puts the dominant in a position of power, but to others in the room, it still appears to be a natural position to sit in. In situations where sitting on the floor may be seen as out of the ordinary, though, it may be more fitting for the submissive to just rest their head on their dominant's shoulder, against his arm, or on his lap; this allows the submissive's head to still be lower than the dominant's head, but again, could be assumed to be a very natural position, and only those involved will know the real significance of the seating arrangement.
In life, you don't always have to be extreme, being kinky at one moment and having to be totally vanilla the next. It is possible to have the best of both worlds.
Thanks for reading! I will post part two if anybody is interested.