funch, skyskraper's suggestion is good. You can use the V+ and V- leads from your PSU, and take the virtual ground (IG on the M³ board) to power your Hagerman Bugle phono board. Leave the Welborne PS1's ground unconnected.
Looking at the Bugle schematic, it does not source or sink significant current from the virtual ground so the TLE2426 on the M³ board will have no problem with the additional "load". Moreover, the Bugle consists of three OPA2130 dual opamps. These opamps are very low current devices (~530uA per amplifier), so in total it adds only about 3.5mA to the total current draw on the PSU, which is essentially nothing. Even if you change to use AD8066s on the Bugle, the additional current draw is only ~6.6mA * 6 = 40mA. The Welborne PS1 should have no trouble powering both the M³ and the Bugle.