ion-molecular bond is just refering to one of those inter-particle bonds. I'm just catergorising bonds by what they bind to.
Bridge bond is a multi-centered bonding. A normal covlant bond involves 2 nulcei. a bridge bond involes at least 3 nulcei. Bridge bonding is common in the borane family. I had included a picture of it below. I'm not well-versed in bridge bonding. It's relatively a new idea/concept to me still.
Apparently, there is a new type of chemical bond call the "Catch Bond", discovered by scientists from Georgia Institute of Technology. I think you better do a Google on it, because I'm not too sure about it myself.