You have several options available, with each option involving some kind of PC hardware to interface with your Arinc429 bus. I am mostly using PCI cards in PC-based LabVIEW applications or RS232-to-Arinc429 adapters to interface with Arinc429 bus. You could also use a PXI-based system but this is going to be more expensive. Here are a few manufacturers, where you could get ARINC429 PCI/PXI interfaces: Condor Engineering, Excalibur, and Data Device Corporation (DDC). Each one provides LabVIEW drivers for their cards.
Another option is to use an RS232-to-Arinc429 adapter. This is basically a device that plugs into your serial port on the PC and interfaces with the Arinc429 bus. I am using a device from RTX Systems. The device comes with a DLL, and you can access all its functionality using DLL functions from LabVIEW. If you are using a non-Windows OS, then you can still talk to the device by writing directly to the serial port. In that case, you will have to handle the conversion from RS232 bytes to Arinc429 words. I have created a LabVIEW driver for both the DLL function calls and direct RS232 access from LabVIEW.
Each option will involve around $2000 (more or less) for 2/2 TX/RX channels pluse the development time for software.