What is the process, and how long does it take, to go back onto active duty? Is there a way to expedite my reenlistment?

Transfering back to active from reserve (conditional release) is time consuming. SGM McCloud outlined the steps you need to take to make the REQUEST (it is not guarenteed that your GO will approve it). https://armyeitaas.sharepoint-mil.us/teams/usar-g1-pag/Lists/ActionsList/USARG1PAG.aspx?FilterField1=Category&FilterValue1=20%20%2D%20Conditional%20Releases&FilterType1=Choice&FilterDisplay1=20%20%2D%20Conditional%20Releases&FilterField2=ActionType&FilterValue2=TPU&FilterType2=Lookup&FilterDisplay2=TPU&viewid=780e2707%2D33a0%2D47e8%2D84ef%2D1b83c0cd7972
There have been multiple issues transfering betwene branches with IPPSA. There are multiple things that have to happen to assign you to the reserves and get your pay set up before a bonus can be process/payed out.

We could use an update on the rest; did you finish that CDL program?

For that USAR bonus, your unit doesn't have to just give you the runaround, the AGR can just show you what step it's at now here:
https://xtranet/usarc/g8/pay/Bonus%20Report/Forms/AllItems.aspx
Pro tip: sometimes a unit AGR is lackluster, and gets ambivalent and gets behind on things like pay. Not saying that's the case here, just be prepared to deal with an AGR who hasn't completed the first unit step on bonus payment.

The process to go back to active duty starts with you contacting an AD recruiter. And filling out a DD 368 conditional release. The Recruiter fills out the MEPS info and signs it, then you need your first GO in USAR to approve it before you can contract AD. That GO signature could take 2-6 months, and probably requires a memo from you, discussing your financial situation AND your desire to continue a career on AD.
Once you have that approved DD 368, you have 6 months to get a contract and orders, but that piece usually takes 1-3 months.
The current In and Out Calls will determine if you get to go back as an MP or get a new MOS.

Merry Christmas.

Since no one has mentioned it, have you checked with your unit about Active Duty Special Works and Active Duty Operational Support? These would not be nearly the hassle to make happen if they are available and while they are listed as Temporary, some get funded year after year. Talk to your Career Manager.