Encrypt an external hard drive with read+write access on both Windows and Linux

Some possibilities are described below.

LUKS encryption on Windows

You may use the Linux LUKS disk encryption also from Windows. To enable Windows to work with LUKS use LibreCrypt. This project is still maintained, although the author is thinking about a rewrite to solve some security issues.

Bitlocker encryption on Linux

The project that enables non-TPM Bitlocker on Linux is cryptsetup, which now has an initial support for Bitlocker. Read more about it in the article Encryption Tool for Windows and Linux.

CipherShed - another TrueCrypt fork

The open-source project CipherShed is available for Windows, Mac OS X and GNU/Linux. As packages for OS X and Linux do not exist yet, compile from source is required for those platforms.

Cryptomator - cloud alternative

The open-source Cryptomator is a tool for encrypting data stored on cloud providers, as alternative to USB disks. Available for Windows, macOS, Linux, Android and iOS.

Use Veracrypt. It's development is steady, of exceedingly high quality, and multi-platform.

Here's an article from 2016 describing how to encrypt a flash drive. Will be the same process for an external hard drive. Enjoy. https://www.esecurityplanet.com/open-source-security/how-to-encrypt-flash-drive-using-veracrypt.html

Out of the box, no.

Bitlocker is one option, but it's only available in Pro editions of Windows and Linux support is not proven reliable, as you've noticed. In my experience Dislocker works okay, but please be aware that the last official release doesn't support Bitlocker's newer, stronger encryption added in recent (190x?) versions of Windows 10. The support was added on master branch, but it wasn't released yet.

Consider Truecrypt or Veracrypt. They are Windows-native 3rd party encryption solutions (VC is a fork of TC) with good Linux support: official Linux ports are available, but there's also support by cryptsetup which is Linux's de facto standard disk encryption tool.