How to display a form filled by a VBO-submission?
As per the "I'm not very experienced in development", you may want to use an alternative approach which only requires site building skills, as further explained below ...

Use the integration of the Privatemsg module with Rules instead (make sure to checkout this community docu, and its child pages ...), together with the Views Bulk Operations module.

For more details, refer to the video about Using Rules components with VBO. Possibly you also want to look at the 2 prior videos and/or the 2 subsequent videos (all about Views Bulk Operations), i.e.:


Introducing Views Bulk Operations.
More details about VBO settings.
Using Rules componens with more than one parameter.
Using VBO to load list of objects into Rules.


In this specific case;


use Views bulk operations to create the list of your users to be targeted (so this is just a minor variation of the VBO based view you seem to already have in place).
create a Rules Component which uses Rules action "Send a message" (provided by the Privatemsg module). If you'd add 2 "variables" to this Rules Component, named something like "MsgSubject" and "MsgBody", you might want to use those variables as "tokens" for constructing the actual Subject and Body of your message.
Within your VBO settings, just execute this Rules Component. If you then use this VBO-view, you can specify the desired values for the variables used to create your Rules Component (like "MsgSubject" and "MsgBody"). So you avoid hardcoding the "Subject" and "Body" for the "Send a message" action (without those variables it would only allow you to send predefined messages). And this simply by using these variables of your Rules Component (to implement that "Subject" and "Body" of the message). That way, each time you use your VBO to send such messages, you can enter the desired "Subject" and "Body" for each of those messages.


Done, no (custom coding) involved ...

For some other illustrations about using VBO in combination with Rules Components, refer to the answers to these questions:


How to bulk update select list fields?
How to bulk delete selected content/nodes?