Q:

Get list of markers in bounds in React Native

How to get list of markers in specific bounds in react-native-maps?

A:

This is not specific to react-native-maps. 
In order to check markers in specific bounds you can use for example mapbox/cheap-ruler library. 
The function you are looking for is insideBBox
You can also do it in pure javascript 
if( bb.ix <= p.x && p.x <= bb.ax && bb.iy <= p.y && p.y <= bb.ay ) {
    // Point is in bounding box
}

bb is the bounding box, (ix,iy) are its top-left coordinates, and (ax,ay) its bottom-right coordinates. p is the point and (x,y) its coordinates.
So: 

Loop on your array of markers 
Use one of the options above (cheap-ruler or pure js)
Get the new list of markers inside the bounding box
Update your React Native state using setState

