If you want to follow the progress of the bill, you can do so via the Texas Legislature's web site for looking up bills.
Now the article doesn't list the bill numbers or anything useful like that. So I would contact the co-author's office, Rep. James Frank, and ask for the House bill number, and what the companion bill number is for the Senate.
The article was from the 5th, so almost two weeks ago, so it may have passed out of the House by now, and also out of the Senate committee.
So, call Rep Frank's office, say this impacts you and you support it, and ask for bill numbers and such.
https://www.texastribune.org/directory/james-frank/If you type the bill number into the upper right section on this page, you can lookup the status of it:
https://capitol.texas.gov/MnuCommittees.aspxOnce you find out where the bill is, and the status, you can start contacting elected officials to ask for their support in moving the bill out. If you know of others who also homeschool, and are interested in this bill, get them to work with you on contacting reps - best way I've found is to take the lead on emails to reps, copy all your friends as the CC, then just ask them to Reply All, with their comments on the issues.
Let us know if you need any other tips on working with the Legislature - a lot of us on here have gotten pretty good with our hobby lobby efforts for Constitutional Carry, and we can help you out. It's pretty late in the session, which ends this month, so things need to be moving or just about done to have a chance to pass. So time is of the essence.
Good luck.