Depending on the age of the house, it is possible that the dryer 10-30 receptacle is in fact fed by 10/3 with ground NM cable (4 conductors total), and the installer used a 10-30 receptacle to match an existing dryer plug or due to lack of knowledge. This is not so likely, but if it is the case, that's good. In this case it would be worth switching the dryer receptacle and cord to 14-30, and removing the bonding strap in the dryer.
If you want to share a single circuit between the dryer and the EVSE, that is definitely possible if you have separate neutral and ground (4 conductors total). It's probably OK if you have only three conductors total (2 hots and a neutral) but the circuit originates at a main panel with service disconnect, where the neutrals and grounds are interconnected.
But you would need a method to keep both the dryer and the EVSE from running at once. So you need to install at a minimum a 30 amp DPDT snap switch, such as the Leviton 1288. One side of the snap switch powers a dryer receptacle, either 14-30 if you have 4 total conductors or 10-30 if you have 3 total conductors. The other side powers an EVSE receptacle, preferably 6-30, but 14-30 could be used if you have 4 total conductors. The EVSE receptacle could also be a -50 version (50 amp) if that is preferred, or it could be hardwired. The EVSE, however, would need to be sized for the 30 amp circuit, so set to no more than 24 amps.
All in all that's a bit of trouble, so I would say it only makes sense when running a new circuit would be alot more trouble. If only a little more trouble, run a new circuit.
Cheers, Wayne