When you start R from the command line and then run system(echo $PATH), you are inheriting the Bash environment from your command line session. When you launch RStudio from, say, the Dock or Finder on a Mac or as a system application in Ubuntu, and not from the command line, RStudio does not gets its environment from your /.bashrc. Instead it will get the environment variables from system-wide settings. How it finds those system settings will depend on the operating system.
Ubuntu
See this explanation of environment variables in Ubuntu, especially the section on desktop applications.
According to that explanation:
You can add an environment variable to an application by editing its .desktop file. For example, to run "digiKam" with the environment variable APPMENU_DISPLAY_BOTH=1, find the corresponding digikam.desktop file and add the setting of the variable, via the env command, to the entry "Exec":
The RStudio .desktop file will be in ~/.local/share/applications/ or /usr/share/applications/ (most likely the latter). Edit that file to include this line:
PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games;/path/to/bcftools-1.2/htslib-1.2.1/tabix
Mac
System-wide environment variables are set by the Launch Agent and not by Bash. Exactly how you set the environment variables for applications launched from the Finder will depend on your version of Mac OS X. This answer might help.
The way that I do this is to add a file, ~/Library/LaunchAgents/com.username.envvariables.plist with these contents:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>Label</key>
<string>com.username.envvariables</string>
<key>ProgramArguments</key>
<array>
<string>sh</string>
<string>-c</string>
<string>
launchctl setenv PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games;/path/to/bcftools-1.2/htslib-1.2.1/tabix
</string>
</array>
<key>RunAtLoad</key>
<true/>
</dict>
</plist>
You will then have to load that file:
launchctl load ~/Library/LaunchAgents/com.username.envvariables.plist
You may have to restart the Finder:
killall -KILL Dock
Then restart RStudio.