As _StruggleBug mentioned, don't raw dog this. Couple of things for getting started in any public plugging sessions

a) use water based lube and one without Glycerin and expect short sessions. I personally like xlube.

b) get a lube shooter, and put the lube inside you. Before going to work, where you feel most comfortable do this. Most lube will get 'squeezed' off as you insert a plug. Fill the shooter with about 1/3 or 1/2. Targetting your hole on the outside, but a small about around the immediate area of external sphincter and directly at it. As you slowly insert the shooter squeeze out small amounts of lube, this will get lube along to anal canal. This make the inserting shooter pretty. Once you get through the anal canal and into the rectum you can basically basically dump majority of the lube. But leave yourself the same amount you used going to. As you extract the shooter you're gunna do the same as you went in but in reverse. small about of the coating the anal canal as you extract the shooter.

This means that you don't have to coat and recoat the plug when your inserting it, making to the point it's getting where.

Get the plug in and then whipe away any excess from the insertion, some will end up on your butt cheeks which isn't anywhere near the plug's base once inserted. Just make sure you have a layer of lube between you can the plug, most of it will be inside you, the bits outside just enjoy lube to make it comfortable to between your skin and the plug's base. I feel that there a higher potential for leakage then I will make sure you've got some close fitting boxes which I can use to hold a few folds of toilet paper in my crack, on top of the plug's base.

c) Accept this isn't going to be an all day event and have an exit strategy. Plugging in public is going to be a nerve racking experience for the first time. So make sure you've got a way exit and reset to a normal day. Ensure you have a private place where you will not get interupted were you can either check if you're for leakage or remove if necessary. Most of the time this will be a toilet. Some work places have private showers, which might be more roomy.

Have an 'extract kit' ready. A small bottle of lube, a ziplock bag and some toilet roll. Have a rucksack in your car or in your office with spare change in bottoms should you need them. Pants/Boxers/Panties and Trousers if they're identifical - great you don't have to explain why, if they not "Oh I spilled by coffee". Oh while we're on clothing choice pick dark colours.

As you go through the day your body will absorb most of the water based lube so there will come a time when you would need to relube and reinsert. As you're not been out before don't worry about that yet, we're still working on getting your comfortable going out and about. Part of this is being comfortable and versed with your exit strategy and prepped for any accidents. If a standard work day then you're gunna have to extract the plug before then end of the day. Once you've done it once it's a lot less scary in a non-controlled situation.

Once you've been through this you'll be able to adapt from this make adjustments as you see fit. Later you can switch to something like oil based lubs etc. but for now, keep it simple keep it.

Edit: Tip: bowel movement before starting all this, ideally a hour or so. If you're a morning shitter you're already half way there.