To make it short, it is not possible to download BlueStacks in a portable version. Those responsible for this software have versions for macOS and Windows, but there is nothing beyond that. These two versions require a traditional installation, and therefore, cannot be considered portable in any way.
You should also keep in mind that BlueStacks works like a virtual machine, which means that it needs several heavy files to work properly. The idea of a portable is to condense an installation as much as possible in a folder that weighs little and that you can take with you everywhere, so the option of creating a "slimmed down" version of BlueStack is not even viable.
You may still find websites on the Internet that claim you can get portable versions of BlueStacks from their download links. Well: if you find something like that, be suspicious. Firstly, it can be malware that someone with bad intentions may want to use to infect your computer, which could have negative consequences for your computer or, even worse, your data.
Secondly, if someone has created a BlueStacks executable that can function as a portable, that person will have violated the terms and conditions of use of the software and may be prosecuted by the appropriate authorities. If you choose to use it, you may meet the same fate.
Having portable versions of different programs is indeed very convenient since they weigh little, do not require installation, and you can take them anywhere. Unfortunately, there are not many companies who choose the portability route, and BlueStacks is certainly not one of them.