Is there a time limit for Medicaid when changing states?

Look at state Medicaid site to see just what the waiting period is. I bet 60 days. FL is pretty user friendly for elders as so many move there or are snowbirds.
BUT
She will need to do whatever to become a legal resident of the state of FL. Like get FL driver’s license or state ID; get her mailing address switched from CA to FL.... eg get everything from CMS / MediCARE & her banking & SSA info to her new FL address.

in theory she could apply for Medicaid upon entering FL, but it’s going to ime cause constant hiccups with FL Medicaid unless she definitively does this. As her “legal” address is in CA so inevitably paperwork is going to go to CA. & that snowballs into missing deadline, yada, yada.

if she right now is with a bank that has a presence in FL lucky her.

As an aside on all this, try to do a realistic take on what your moms “needs” are and what you thinking that FL Medicaid could provide AND cross that with what your mom’s financial are. Medicaid is a huge program..... like everything from kids dental care under CHIP to loaning breast pumps via WIC to long term care in a NH. And each state runs its Medicaid program uniquely within an overall federal guidelines. AND for every program there will be a “needs determination” to see if she meets criteria BOTH medically and financially for the specific Medicaid program.
SO
If your hope is that she goes into a NH, she’s going to have to have a nice fat medical chart that clearly & overwhelmingly shows her need for skilled nursing care in a facility and she’s sufficiently impoverished for LTC Medicaid. That’s a whole different situation that if she’s going onto community based Medicaid and enrolling into a PACE / day program for her medical care & daily activities or getting into an IHHS / in home health services do have outside contractor with FL Medicaid that comes to see her 2-3 maybe 4 days at week for a few hours in your home as she lives with you.

You may find that having mom get a needs assessment done will be something to do ahead of ever applying for Medicaid as this way you can have her apply just for programs she will 4sure meet the medical criteria for. And then in tandem have her do whatever legit spend down needed to meet the Medicaid financial criteria for as well.

Look at her MediCARE as well. If she has switched to a Medicare Advantage plan those just do not cross state lines. So she will need to find a new Medicare Advantage plan for FL.
BUT
If she’s on original Medicare and has a gap / supplemental for 2ndary, she needs to see if that underwriter does polices in FL that she can do a transfer into. Some of the bigger ones - like United - will have gap plans in FL that will be similar or identical to her old CA based supplemental. It may have a premium different but at least it flows over.

Also please please do get mom to do fresh legal (will, DPOA, advance directives) by a FL attorney. Yeah it will be overwhelming to deal with, get a couple of binders going so you stay organized so less stress. Good luck.