Are griefers blowing up your crates in full public sessions constantly? Are your precious investments which cost several thousand in GTA $ going up in smoke because some asshole won't quit? Are your associates simply not enough protection to deal with all the bastards who find their way Online? Bothered by the fact that you can't run buy and sell missions in private or crew lobbies?
Worry not! Getting into a private session all on your own in order to avoid the griefers and various connection issues brought on by the dodgy internet connections of other players (which affects you because of the peer-to-peer server architecture) is pretty simple.
Depending on what platform you're on or how you're connected to the internet, there are various ways of kicking everyone from your session - of course, in reality, they stay in their communal session and you will be booted to a public session of your own, but let's keep terminology simple.
Naturally, the first step of this is to actually get into a public lobby. Once in, you'll need to go to your corporate headquarters which keeps you in the same session, but a separate instance.
Cable Unplug (All Platforms)
This is the easiest method and all and so we suggest you try it first. Simply either fiddle with your modem's coaxial cable, disconnecting and reconnecting it quickly, or unplug the DSL cable from your router for a few seconds and plug it back in.
This should kick you out of lobbies with other players and put you in one alone, the game thinks you are lagging/on a poor connection and doesn't want you to affect the performance of other players.
Mobile Portable Hotspot (All Platforms)
If you are using Wi-Fi, instead of connecting directly, you should use your smartphone to create a portable hotspot, connect to the Wi-Fi with the phone and to the phone with the console. Then, either turn off Wi-Fi (not the hotspot) on your phone, or switch to mobile data.
Then again, seeing as GTA Online isn't actually bandwidth heavy, you could simply use mobile data for playing anyway and switch it off and on again while in your HQ.
If you are on PS4, you can also do the following while in your public lobby. Go Settings --> Network --> Choose Network --> Custom.
Leave everything as is, but for MTU, enter 800. Just remember to undo this setting if you want to play another game or join a public lobby!
While in your public lobby, go to Settings --> Network Settings --> Test NAT Type. Wait a while and then go back into the game. You should be in a solo session.
Load into a public session, ALT+TAB out of the game and open the task manager either with CTRL+SHIFT+ESC or by running it from the start menu.
In the task manager, navigate to the Performance tab where you will see "open Resource Monitor" on the bottom. Click on this, and wait for all the running programs to load up. You'll see GTA5.exe in the list, which you need to right click, and in the context menu click on Suspend Process. Wait a couple of seconds, and click on Resume Process in the context menu - voilá, solo public session!
All of these methods will boot you into a public lobby of your own. Take note that waiting too much in between re-plugging cables or turning your internet back on will simply disconnect you from the game entirely. In some cases, simply changing your NAT settings will also achieve the desired result, but that is a bit of a gamble.
If you're using cable internet, then unplugging the ethernet cable on consoles will simply disconnect you from GTA Online, however on PC this method allows you to enter your own public lobby. Another option is blocking port 6672 using Windows Firewall, however this is a toss-up between getting your own lobby or getting kicked.
Depending on your router, you can also manually restrict internet access for certain IPs. This works for all platforms, you just need to restrict the IP of your device for a few second and voila, you are in your own GTA Online session.
Some players also suggest simply switching to free-aim. You need to get into singleplayer GTA 5, set free-aim as your preferred aim method and switch back to Online. Only a tiny fraction of the community plays free-aim anyway and barely any of them are griefers.
GTA Online's griefer problem is an affliction of the community, not the game. Bored idiots who can only entertain themselves by ruining the fun of others with (granted, poorly balanced) vehicles really can't be blamed on Rockstar here.
Have you had any luck running delivery missions in populated public GTA Online lobbies, or do you stick to those where you are alone?