Train from Penrith,England to Edinburgh, Scotland

As long as you don't have an unreasonable amount of luggage, the easiest is just to walk between the stations in my opinion. But there are buses as well.

Unless you really don’t like travelling part of the journey by bus, I would get off the 11.17 train at Lockerbie and take the rail replacement bus direct to Edinburgh. You will arrive 8 minutes later than taking the train via Glasgow but will not have the hassle of changing stations there. It looks like you can secure the route through Lockerbie for less than £30 if you book now.
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The bus between the two Glasgow stations is the #398- the free inter station bus, which runs every 10 minutes. It takes 5 minutes between the stations.
You can walk the distance in the time you are waiting for the bus, but if you have luggage or its raining may as well use the bus as it's free.
If you leave Penrith at 1151 you arrive 30 minutes later, but pay £18.50 as opposed to £33.80 on the 1117.

Thank you for all this info.
I did consider the bus choice & was confused. It says there's 23 minutes connection time. Is the rail replacement bus close to the Lockerbie train station?

Also thank you for the choices regarding either walking or taking the #398- free inter station bus in Glasgow. There's always a bit more to consider when one is traveling solo & I plan to make a decision hopefully in the next few hours.

My senior railcard expires July 4 & I'm traveling July 6 but I am also assuming there would be no grace period of 2 days extra ?

No grace period for the railcard.

The stop at Lockerbie is right outside the station door - level access through the ticket office from the northbound platform. The bus originated at Carlisle at 1135.

Last year traveling around England I encountered a few train delays & because I didn't give myself enough time between connections I missed a few connections. If for some reason my train to Lockerbie was delayed & I missed the bus to Edinburgh do you think I could find another bus on Sunday, July 6 ? I like the idea of not having to go into Glasgow but want to be sure to have a backup if I miss the bus from Lockerbie to Edinburgh.
Do you recommend I purchase ticket from Scotrail or TransPennine Express ?
Thank you

Thank you everyone for all your advice/ help.
I purchased my ticket & decided Penrith to Lockerbie via train then connecting bus to Edinburgh.

As it is a rail replacement bus, and oddly doesnt connect at Carlisle it should wait. However the rail replacement bus is then at 10 minutes past each hour until 2310.
If the initial train was very late such as the connection would fail then my fall back preference would be to change at Carlisle into the next available bus. A bigger town, more staff and a well established queing system.
Lockerbie slightly worries me in case of abnormally high numbers of passengers, and not knowing if they will have a stand by bus on site. Carlisle always have stand by buses on site to cater for excess loads.